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Mathematics Quiz - Class 9 Mathematics Sequences and Prog...

Question 1/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(a_1=3\) और \(a_n=2a_{n-1}+n+1\) है। \(a_4\) का मान क्या होगा?

In a sequence, \(a_1=3\) and \(a_n=2a_{n-1}+n+1\). What is the value of \(a_4\)?

Explanation opens after your attempt

Correct Answer

C. उनचास(49)

Step 1

Concept

We get \(a_2=9\), \(a_3=22\), and \(a_4=49\). In exams, keep the current value of (n) correct.

Step 2

Why this answer is correct

The correct answer is C. उनचास / (49). We get \(a_2=9\), \(a_3=22\), and \(a_4=49\). In exams, keep the current value of (n) correct.

Step 3

Exam Tip

\(a_2=9\), \(a_3=22\) और \(a_4=49\) मिलता है। परीक्षा में (n) का वर्तमान मान सही रखें।

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Question 2/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(b_1=6\) और \(b_n=3b_{n-1}-n\) है। \(b_4\) का मान क्या होगा?

In a sequence, \(b_1=6\) and \(b_n=3b_{n-1}-n\). What is the value of \(b_4\)?

Explanation opens after your attempt

Correct Answer

B. एक सौ इकतीस(131)

Step 1

Concept

We get \(b_2=16\), \(b_3=45\), and \(b_4=131\). In exams, handle both multiplication and subtraction carefully.

Step 2

Why this answer is correct

The correct answer is B. एक सौ इकतीस / (131). We get \(b_2=16\), \(b_3=45\), and \(b_4=131\). In exams, handle both multiplication and subtraction carefully.

Step 3

Exam Tip

\(b_2=16\), \(b_3=45\) और \(b_4=131\) मिलता है। परीक्षा में गुणा और घटाव दोनों ध्यान से करें।

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Question 3/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(c_1=1\), \(c_2=3\) और \(c_n=2c_{n-1}+c_{n-2}\) है। \(c_5\) का मान क्या होगा?

In a sequence, \(c_1=1\), \(c_2=3\), and \(c_n=2c_{n-1}+c_{n-2}\). What is the value of \(c_5\)?

Explanation opens after your attempt

Correct Answer

D. इकतालीस(41)

Step 1

Concept

We get \(c_3=7\), \(c_4=17\), and \(c_5=41\). In exams, do not interchange the previous two terms.

Step 2

Why this answer is correct

The correct answer is D. इकतालीस / (41). We get \(c_3=7\), \(c_4=17\), and \(c_5=41\). In exams, do not interchange the previous two terms.

Step 3

Exam Tip

\(c_3=7\), \(c_4=17\) और \(c_5=41\) मिलता है। परीक्षा में पिछले दो पदों का क्रम न बदलें।

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Question 4/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(d_n=d_{n-1}+2n\) और \(d_4=25\) है, तो \(d_1\) का मान क्या होगा?

If \(d_n=d_{n-1}+2n\) and \(d_4=25\), what is the value of \(d_1\)?

Explanation opens after your attempt

Correct Answer

A. सात(7)

Step 1

Concept

\(d_4=d_1+4+6+8\), so \(d_1=7\). In exams, apply the same rule backward too.

Step 2

Why this answer is correct

The correct answer is A. सात / (7). \(d_4=d_1+4+6+8\), so \(d_1=7\). In exams, apply the same rule backward too.

Step 3

Exam Tip

\(d_4=d_1+4+6+8\), इसलिए \(d_1=7\) है। परीक्षा में पीछे की ओर भी वही नियम लागू करें।

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Question 5/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

अनुक्रम (4), (9), (19), (39) के लिए कौन-सा पुनरावर्ती नियम सही है?

Which recursive rule is correct for the sequence (4), (9), (19), (39)?

Explanation opens after your attempt

Correct Answer

B. नियम \(e_n=2e_{n-1}+1\)Rule \(e_n=2e_{n-1}+1\)

Step 1

Concept

Each new term is obtained by doubling the previous term and adding (1). In exams, test the rule on two terms.

Step 2

Why this answer is correct

The correct answer is B. नियम \(e_n=2e_{n-1}+1\) / Rule \(e_n=2e_{n-1}+1\). Each new term is obtained by doubling the previous term and adding (1). In exams, test the rule on two terms.

Step 3

Exam Tip

हर नया पद पिछले पद के दोगुने में (1) जोड़ने से मिलता है। परीक्षा में नियम को दो पदों पर जाँचें।

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Question 6/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(f_1=10\) और \(f_n=f_{n-1}-n\) है, तो पहला ऋणात्मक पद कौन-सा होगा?

If \(f_1=10\) and \(f_n=f_{n-1}-n\), which will be the first negative term?

Explanation opens after your attempt

Correct Answer

D. पाँचवाँ पद(5)

Step 1

Concept

\(f_2=8\), \(f_3=5\), \(f_4=1\), and \(f_5=-4\). In exams, find the first term that goes below zero.

Step 2

Why this answer is correct

The correct answer is D. पाँचवाँ पद / (5). \(f_2=8\), \(f_3=5\), \(f_4=1\), and \(f_5=-4\). In exams, find the first term that goes below zero.

Step 3

Exam Tip

\(f_2=8\), \(f_3=5\), \(f_4=1\) और \(f_5=-4\) है। परीक्षा में शून्य से नीचे जाने वाला पहला पद देखें।

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Question 7/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(g_1=2\) और \(g_n=g_{n-1}+2n-1\) है। \(g_5\) का मान क्या होगा?

In a sequence, \(g_1=2\) and \(g_n=g_{n-1}+2n-1\). What is the value of \(g_5\)?

Explanation opens after your attempt

Correct Answer

A. छब्बीस(26)

Step 1

Concept

Adding (3), (5), (7), and (9) gives \(g_5=26\). In exams, write the added quantities separately.

Step 2

Why this answer is correct

The correct answer is A. छब्बीस / (26). Adding (3), (5), (7), and (9) gives \(g_5=26\). In exams, write the added quantities separately.

Step 3

Exam Tip

क्रमशः (3), (5), (7), (9) जोड़ने पर \(g_5=26\) मिलता है। परीक्षा में जोड़ी गई राशियों को अलग लिखें।

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Question 8/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(h_1=3\) और \(h_n=n h_{n-1}\) है, तो \(h_4\) का मान क्या होगा?

If \(h_1=3\) and \(h_n=n h_{n-1}\), what is the value of \(h_4\)?

Explanation opens after your attempt

Correct Answer

C. बहत्तर(72)

Step 1

Concept

\(h_2=6\), \(h_3=18\), and \(h_4=72\). In exams, multiply by (n) at each step.

Step 2

Why this answer is correct

The correct answer is C. बहत्तर / (72). \(h_2=6\), \(h_3=18\), and \(h_4=72\). In exams, multiply by (n) at each step.

Step 3

Exam Tip

\(h_2=6\), \(h_3=18\) और \(h_4=72\) होता है। परीक्षा में हर चरण में (n) से गुणा करें।

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Question 9/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(j_1=1\) और \(j_n=j_{n-1}+n^2\) है। \(j_4\) का मान क्या होगा?

In a sequence, \(j_1=1\) and \(j_n=j_{n-1}+n^2\). What is the value of \(j_4\)?

Explanation opens after your attempt

Correct Answer

B. तीस(30)

Step 1

Concept

\(j_4=1+4+9+16=30\). In exams, calculate \(n^2\) first.

Step 2

Why this answer is correct

The correct answer is B. तीस / (30). \(j_4=1+4+9+16=30\). In exams, calculate \(n^2\) first.

Step 3

Exam Tip

\(j_4=1+4+9+16=30\) है। परीक्षा में \(n^2\) का मान पहले निकालें।

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Question 10/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(k_1=64\) और \(k_n=\frac{k_{n-1}}{2}+n\) है, तो \(k_4\) का मान क्या होगा?

If \(k_1=64\) and \(k_n=\frac{k_{n-1}}{2}+n\), what is the value of \(k_4\)?

Explanation opens after your attempt

Correct Answer

D. चौदह(14)

Step 1

Concept

\(k_2=34\), \(k_3=20\), and \(k_4=14\). In exams, add (n) after dividing.

Step 2

Why this answer is correct

The correct answer is D. चौदह / (14). \(k_2=34\), \(k_3=20\), and \(k_4=14\). In exams, add (n) after dividing.

Step 3

Exam Tip

\(k_2=34\), \(k_3=20\) और \(k_4=14\) मिलता है। परीक्षा में भाग देने के बाद (n) जोड़ें।

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Question 11/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(m_1=2\) और \(m_n=m_{n-1}+3n\) है। \(m_4\) का मान क्या होगा?

In a sequence, \(m_1=2\) and \(m_n=m_{n-1}+3n\). What is the value of \(m_4\)?

Explanation opens after your attempt

Correct Answer

A. उनतीस(29)

Step 1

Concept

\(m_4=2+6+9+12=29\). In exams, start adding from (n=2).

Step 2

Why this answer is correct

The correct answer is A. उनतीस / (29). \(m_4=2+6+9+12=29\). In exams, start adding from (n=2).

Step 3

Exam Tip

\(m_4=2+6+9+12=29\) है। परीक्षा में जोड़ (n=2) से शुरू करें।

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Question 12/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(n_1=5\) और \(n_n=2n_{n-1}-n^2\) है, तो \(n_4\) का मान क्या होगा?

If \(n_1=5\) and \(n_n=2n_{n-1}-n^2\), what is the value of \(n_4\)?

Explanation opens after your attempt

Correct Answer

C. ऋण दस(-10)

Step 1

Concept

\(n_2=6\), \(n_3=3\), and \(n_4=-10\). In exams, do not stop the calculation when a negative answer appears.

Step 2

Why this answer is correct

The correct answer is C. ऋण दस / (-10). \(n_2=6\), \(n_3=3\), and \(n_4=-10\). In exams, do not stop the calculation when a negative answer appears.

Step 3

Exam Tip

\(n_2=6\), \(n_3=3\) और \(n_4=-10\) है। परीक्षा में ऋणात्मक उत्तर आने पर भी गणना न छोड़ें।

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Question 13/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(r_1=1\), \(r_2=2\) और \(r_n=r_{n-1}+3r_{n-2}\) है, तो \(r_5\) का मान क्या होगा?

If \(r_1=1\), \(r_2=2\), and \(r_n=r_{n-1}+3r_{n-2}\), what is the value of \(r_5\)?

Explanation opens after your attempt

Correct Answer

B. छब्बीस(26)

Step 1

Concept

\(r_3=5\), \(r_4=11\), and \(r_5=26\). In exams, multiply the second previous term by (3).

Step 2

Why this answer is correct

The correct answer is B. छब्बीस / (26). \(r_3=5\), \(r_4=11\), and \(r_5=26\). In exams, multiply the second previous term by (3).

Step 3

Exam Tip

\(r_3=5\), \(r_4=11\) और \(r_5=26\) मिलता है। परीक्षा में दूसरे पिछले पद को (3) से गुणा करें।

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Question 14/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(s_1=3\) और (s_n=s_{n-1}+(-1)^n n) है। \(s_5\) का मान क्या होगा?

In a sequence, \(s_1=3\) and (s_n=s_{n-1}+(-1)^n n). What is the value of \(s_5\)?

Explanation opens after your attempt

Correct Answer

D. एक(1)

Step 1

Concept

\(s_2=5\), \(s_3=2\), \(s_4=6\), and \(s_5=1\). In exams, read alternating-sign rules carefully.

Step 2

Why this answer is correct

The correct answer is D. एक / (1). \(s_2=5\), \(s_3=2\), \(s_4=6\), and \(s_5=1\). In exams, read alternating-sign rules carefully.

Step 3

Exam Tip

\(s_2=5\), \(s_3=2\), \(s_4=6\) और \(s_5=1\) है। परीक्षा में चिह्न बदलने वाले नियम को सावधानी से पढ़ें।

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Question 15/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(t_1=x\), \(t_n=t_{n-1}+n\) और \(t_5=24\) है, तो (x) का मान क्या होगा?

If \(t_1=x\), \(t_n=t_{n-1}+n\), and \(t_5=24\), what is the value of (x)?

Explanation opens after your attempt

Correct Answer

A. दस(10)

Step 1

Concept

\(t_5=x+2+3+4+5\), so (x=10). In exams, keep the unknown first term separate.

Step 2

Why this answer is correct

The correct answer is A. दस / (10). \(t_5=x+2+3+4+5\), so (x=10). In exams, keep the unknown first term separate.

Step 3

Exam Tip

\(t_5=x+2+3+4+5\), इसलिए (x=10) है। परीक्षा में अज्ञात प्रथम पद को अलग रखें।

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Question 16/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

अनुक्रम (2), (6), (18), (54) के लिए सही पुनरावर्ती नियम कौन-सा है?

Which recursive rule is correct for the sequence (2), (6), (18), (54)?

Explanation opens after your attempt

Correct Answer

C. नियम \(a_n=3a_{n-1}\)Rule \(a_n=3a_{n-1}\)

Step 1

Concept

Each term is (3) times the previous term. In exams, identify the rule by checking consecutive ratios.

Step 2

Why this answer is correct

The correct answer is C. नियम \(a_n=3a_{n-1}\) / Rule \(a_n=3a_{n-1}\). Each term is (3) times the previous term. In exams, identify the rule by checking consecutive ratios.

Step 3

Exam Tip

हर पद पिछले पद का (3) गुना है। परीक्षा में लगातार अनुपात देखकर नियम पहचानें।

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Question 17/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(v_1=4\) और \(v_n=2v_{n-1}-1\) है, तो \(v_5\) का मान क्या होगा?

If \(v_1=4\) and \(v_n=2v_{n-1}-1\), what is the value of \(v_5\)?

Explanation opens after your attempt

Correct Answer

D. उनचास(49)

Step 1

Concept

\(v_2=7\), \(v_3=13\), \(v_4=25\), and \(v_5=49\). In exams, double first and then subtract (1).

Step 2

Why this answer is correct

The correct answer is D. उनचास / (49). \(v_2=7\), \(v_3=13\), \(v_4=25\), and \(v_5=49\). In exams, double first and then subtract (1).

Step 3

Exam Tip

\(v_2=7\), \(v_3=13\), \(v_4=25\) और \(v_5=49\) है। परीक्षा में पहले दोगुना करें फिर (1) घटाएँ।

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Question 18/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(w_1=0\) और \(w_n=w_{n-1}+2^{n-1}\) है। \(w_5\) का मान क्या होगा?

In a sequence, \(w_1=0\) and \(w_n=w_{n-1}+2^{n-1}\). What is the value of \(w_5\)?

Explanation opens after your attempt

Correct Answer

B. तीस(30)

Step 1

Concept

\(w_5=0+2+4+8+16=30\). In exams, apply the exponent (n-1) correctly.

Step 2

Why this answer is correct

The correct answer is B. तीस / (30). \(w_5=0+2+4+8+16=30\). In exams, apply the exponent (n-1) correctly.

Step 3

Exam Tip

\(w_5=0+2+4+8+16=30\) है। परीक्षा में घात (n-1) को सही लगाएँ।

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Question 19/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(x_1=1\) और \(x_n=2x_{n-1}+n^2\) है, तो \(x_3\) का मान क्या होगा?

If \(x_1=1\) and \(x_n=2x_{n-1}+n^2\), what is the value of \(x_3\)?

Explanation opens after your attempt

Correct Answer

C. इक्कीस(21)

Step 1

Concept

\(x_2=6\) and \(x_3=21\). In exams, double the previous term before adding the square.

Step 2

Why this answer is correct

The correct answer is C. इक्कीस / (21). \(x_2=6\) and \(x_3=21\). In exams, double the previous term before adding the square.

Step 3

Exam Tip

\(x_2=6\) और \(x_3=21\) मिलता है। परीक्षा में वर्ग जोड़ने से पहले पिछले पद को दोगुना करें।

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Question 20/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(y_1=7\) और (y_n=y_{n-1}+(n-1)²) है। \(y_5\) का मान क्या होगा?

In a sequence, \(y_1=7\) and (y_n=y_{n-1}+(n-1)²). What is the value of \(y_5\)?

Explanation opens after your attempt

Correct Answer

A. सैंतीस(37)

Step 1

Concept

\(y_5=7+1+4+9+16=37\). In exams, remember to square (n-1).

Step 2

Why this answer is correct

The correct answer is A. सैंतीस / (37). \(y_5=7+1+4+9+16=37\). In exams, remember to square (n-1).

Step 3

Exam Tip

\(y_5=7+1+4+9+16=37\) है। परीक्षा में (n-1) का वर्ग लेना न भूलें।

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Question 21/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(z_1=2\), \(z_2=3\) और \(z_n=z_{n-1}z_{n-2}+1\) है, तो \(z_5\) का मान क्या होगा?

If \(z_1=2\), \(z_2=3\), and \(z_n=z_{n-1}z_{n-2}+1\), what is the value of \(z_5\)?

Explanation opens after your attempt

Correct Answer

D. एक सौ पचपन(155)

Step 1

Concept

\(z_3=7\), \(z_4=22\), and \(z_5=155\). In exams, multiply the two previous terms carefully.

Step 2

Why this answer is correct

The correct answer is D. एक सौ पचपन / (155). \(z_3=7\), \(z_4=22\), and \(z_5=155\). In exams, multiply the two previous terms carefully.

Step 3

Exam Tip

\(z_3=7\), \(z_4=22\) और \(z_5=155\) मिलता है। परीक्षा में पिछले दो पदों का गुणन सही करें।

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Question 22/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(A_1=1\) और \(A_n=nA_{n-1}+1\) है। \(A_4\) का मान क्या होगा?

In a sequence, \(A_1=1\) and \(A_n=nA_{n-1}+1\). What is the value of \(A_4\)?

Explanation opens after your attempt

Correct Answer

B. इकतालीस(41)

Step 1

Concept

\(A_2=3\), \(A_3=10\), and \(A_4=41\). In exams, multiply by (n) and then add (1).

Step 2

Why this answer is correct

The correct answer is B. इकतालीस / (41). \(A_2=3\), \(A_3=10\), and \(A_4=41\). In exams, multiply by (n) and then add (1).

Step 3

Exam Tip

\(A_2=3\), \(A_3=10\) और \(A_4=41\) है। परीक्षा में (n) से गुणा करके (1) जोड़ें।

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Question 23/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(B_1=9\) और \(B_n=B_{n-1}+2^n\) है, तो \(B_4\) का मान क्या होगा?

If \(B_1=9\) and \(B_n=B_{n-1}+2^n\), what is the value of \(B_4\)?

Explanation opens after your attempt

Correct Answer

C. सैंतीस(37)

Step 1

Concept

\(B_4=9+4+8+16=37\). In exams, the addition starts from (n=2).

Step 2

Why this answer is correct

The correct answer is C. सैंतीस / (37). \(B_4=9+4+8+16=37\). In exams, the addition starts from (n=2).

Step 3

Exam Tip

\(B_4=9+4+8+16=37\) है। परीक्षा में जोड़ (n=2) से शुरू होता है।

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Question 24/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(C_1=5\) और (C_n=C_{n-1}+n(n-1)) है। \(C_4\) का मान क्या होगा?

In a sequence, \(C_1=5\) and (C_n=C_{n-1}+n(n-1)). What is the value of \(C_4\)?

Explanation opens after your attempt

Correct Answer

A. पच्चीस(25)

Step 1

Concept

\(C_4=5+2+6+12=25\). In exams, simplify (n(n-1)) first.

Step 2

Why this answer is correct

The correct answer is A. पच्चीस / (25). \(C_4=5+2+6+12=25\). In exams, simplify (n(n-1)) first.

Step 3

Exam Tip

\(C_4=5+2+6+12=25\) है। परीक्षा में (n(n-1)) को पहले सरल करें।

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Question 25/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(D_1=2\) और \(D_n=2D_{n-1}+n-1\) है, तो \(D_4\) का मान क्या होगा?

If \(D_1=2\) and \(D_n=2D_{n-1}+n-1\), what is the value of \(D_4\)?

Explanation opens after your attempt

Correct Answer

D. सत्ताईस(27)

Step 1

Concept

\(D_2=5\), \(D_3=12\), and \(D_4=27\). In exams, add (n-1) separately.

Step 2

Why this answer is correct

The correct answer is D. सत्ताईस / (27). \(D_2=5\), \(D_3=12\), and \(D_4=27\). In exams, add (n-1) separately.

Step 3

Exam Tip

\(D_2=5\), \(D_3=12\) और \(D_4=27\) है। परीक्षा में (n-1) को अलग से जोड़ें।

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Question 26/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(E_1=1\), \(E_2=4\) और \(E_n=E_{n-1}+E_{n-2}+2\) है, तो \(E_5\) का मान क्या होगा?

If \(E_1=1\), \(E_2=4\), and \(E_n=E_{n-1}+E_{n-2}+2\), what is the value of \(E_5\)?

Explanation opens after your attempt

Correct Answer

C. बाईस(22)

Step 1

Concept

\(E_3=7\), \(E_4=13\), and \(E_5=22\). In exams, add (2) after using both previous terms.

Step 2

Why this answer is correct

The correct answer is C. बाईस / (22). \(E_3=7\), \(E_4=13\), and \(E_5=22\). In exams, add (2) after using both previous terms.

Step 3

Exam Tip

\(E_3=7\), \(E_4=13\) और \(E_5=22\) है। परीक्षा में दोनों पिछले पदों के बाद (2) जोड़ें।

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Question 27/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(F_1=20\) और \(F_n=F_{n-1}-2n+1\) है। \(F_5\) का मान क्या होगा?

In a sequence, \(F_1=20\) and \(F_n=F_{n-1}-2n+1\). What is the value of \(F_5\)?

Explanation opens after your attempt

Correct Answer

B. ऋण चार(-4)

Step 1

Concept

\(F_2=17\), \(F_3=12\), \(F_4=5\), and \(F_5=-4\). In exams, understand the subtracted amount as (2n-1).

Step 2

Why this answer is correct

The correct answer is B. ऋण चार / (-4). \(F_2=17\), \(F_3=12\), \(F_4=5\), and \(F_5=-4\). In exams, understand the subtracted amount as (2n-1).

Step 3

Exam Tip

\(F_2=17\), \(F_3=12\), \(F_4=5\) और \(F_5=-4\) है। परीक्षा में घटाई जाने वाली राशि (2n-1) समझें।

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Question 28/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(G_1=3\) और \(G_n=n+2G_{n-1}\) है, तो \(G_4\) का मान क्या होगा?

If \(G_1=3\) and \(G_n=n+2G_{n-1}\), what is the value of \(G_4\)?

Explanation opens after your attempt

Correct Answer

A. बयालीस(42)

Step 1

Concept

\(G_2=8\), \(G_3=19\), and \(G_4=42\). In exams, double the previous term before adding (n).

Step 2

Why this answer is correct

The correct answer is A. बयालीस / (42). \(G_2=8\), \(G_3=19\), and \(G_4=42\). In exams, double the previous term before adding (n).

Step 3

Exam Tip

\(G_2=8\), \(G_3=19\) और \(G_4=42\) है। परीक्षा में (n) जोड़ने से पहले पिछले पद को दोगुना करें।

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Question 29/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(H_1=2\) और (H_n=H_{n-1}+n(n+1)) है। \(H_4\) का मान क्या होगा?

In a sequence, \(H_1=2\) and (H_n=H_{n-1}+n(n+1)). What is the value of \(H_4\)?

Explanation opens after your attempt

Correct Answer

D. चालीस(40)

Step 1

Concept

\(H_4=2+6+12+20=40\). In exams, calculate (n(n+1)) at each step.

Step 2

Why this answer is correct

The correct answer is D. चालीस / (40). \(H_4=2+6+12+20=40\). In exams, calculate (n(n+1)) at each step.

Step 3

Exam Tip

\(H_4=2+6+12+20=40\) है। परीक्षा में (n(n+1)) को प्रत्येक चरण पर निकालें।

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Question 30/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(J_1=50\) और (J_n=J_{n-1}-3(n-1)) है, तो \(J_5\) का मान क्या होगा?

If \(J_1=50\) and (J_n=J_{n-1}-3(n-1)), what is the value of \(J_5\)?

Explanation opens after your attempt

Correct Answer

C. बीस(20)

Step 1

Concept

\(J_5=50-3-6-9-12=20\). In exams, start the subtraction from (n=2).

Step 2

Why this answer is correct

The correct answer is C. बीस / (20). \(J_5=50-3-6-9-12=20\). In exams, start the subtraction from (n=2).

Step 3

Exam Tip

\(J_5=50-3-6-9-12=20\) है। परीक्षा में घटाव (n=2) से शुरू करें।

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Question 31/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(K_1=1\), \(K_2=1\) और \(K_n=2K_{n-1}+K_{n-2}\) है, तो \(K_5\) का मान क्या होगा?

If \(K_1=1\), \(K_2=1\), and \(K_n=2K_{n-1}+K_{n-2}\), what is the value of \(K_5\)?

Explanation opens after your attempt

Correct Answer

B. सत्रह(17)

Step 1

Concept

\(K_3=3\), \(K_4=7\), and \(K_5=17\). In exams, double the previous term and add the term before it.

Step 2

Why this answer is correct

The correct answer is B. सत्रह / (17). \(K_3=3\), \(K_4=7\), and \(K_5=17\). In exams, double the previous term and add the term before it.

Step 3

Exam Tip

\(K_3=3\), \(K_4=7\) और \(K_5=17\) है। परीक्षा में पिछले पद का दोगुना लेकर उससे पहले वाला पद जोड़ें।

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Question 32/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(L_1=6\) और \(L_n=L_{n-1}+2n+1\) है। \(L_5\) का मान क्या होगा?

In a sequence, \(L_1=6\) and \(L_n=L_{n-1}+2n+1\). What is the value of \(L_5\)?

Explanation opens after your attempt

Correct Answer

A. अड़तीस(38)

Step 1

Concept

\(L_5=6+5+7+9+11=38\). In exams, add the odd numbers from (2n+1) correctly.

Step 2

Why this answer is correct

The correct answer is A. अड़तीस / (38). \(L_5=6+5+7+9+11=38\). In exams, add the odd numbers from (2n+1) correctly.

Step 3

Exam Tip

\(L_5=6+5+7+9+11=38\) है। परीक्षा में (2n+1) की विषम संख्याएँ सही जोड़ें।

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Question 33/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(M_1=1\) और \(M_n=3M_{n-1}+n\) है, तो \(M_3\) का मान क्या होगा?

If \(M_1=1\) and \(M_n=3M_{n-1}+n\), what is the value of \(M_3\)?

Explanation opens after your attempt

Correct Answer

D. अठारह(18)

Step 1

Concept

\(M_2=5\) and \(M_3=18\). In exams, add (n) after multiplying by (3).

Step 2

Why this answer is correct

The correct answer is D. अठारह / (18). \(M_2=5\) and \(M_3=18\). In exams, add (n) after multiplying by (3).

Step 3

Exam Tip

\(M_2=5\) और \(M_3=18\) है। परीक्षा में गुणा (3) के बाद (n) जोड़ें।

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Question 34/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(R_1=2\) और \(R_n=nR_{n-1}+n\) है। \(R_4\) का मान क्या होगा?

In a sequence, \(R_1=2\) and \(R_n=nR_{n-1}+n\). What is the value of \(R_4\)?

Explanation opens after your attempt

Correct Answer

C. अठासी(88)

Step 1

Concept

\(R_2=6\), \(R_3=21\), and \(R_4=88\). In exams, both multiply by (n) and add (n).

Step 2

Why this answer is correct

The correct answer is C. अठासी / (88). \(R_2=6\), \(R_3=21\), and \(R_4=88\). In exams, both multiply by (n) and add (n).

Step 3

Exam Tip

\(R_2=6\), \(R_3=21\) और \(R_4=88\) है। परीक्षा में (n) से गुणा और (n) जोड़ना दोनों करें।

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Question 35/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(O_1=4\) और \(O_n=O_{n-1}+2^n+n\) है, तो \(O_4\) का मान क्या होगा?

If \(O_1=4\) and \(O_n=O_{n-1}+2^n+n\), what is the value of \(O_4\)?

Explanation opens after your attempt

Correct Answer

B. इकतालीस(41)

Step 1

Concept

\(O_2=10\), \(O_3=21\), and \(O_4=41\). In exams, add both the power and (n).

Step 2

Why this answer is correct

The correct answer is B. इकतालीस / (41). \(O_2=10\), \(O_3=21\), and \(O_4=41\). In exams, add both the power and (n).

Step 3

Exam Tip

\(O_2=10\), \(O_3=21\) और \(O_4=41\) है। परीक्षा में घात और (n) दोनों जोड़ें।

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Question 36/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(P_1=3\) और \(P_n=P_{n-1}+4n-3\) है। \(P_5\) का मान क्या होगा?

In a sequence, \(P_1=3\) and \(P_n=P_{n-1}+4n-3\). What is the value of \(P_5\)?

Explanation opens after your attempt

Correct Answer

D. सैंतालीस(47)

Step 1

Concept

\(P_5=3+5+9+13+17=47\). In exams, add the numbers formed by (4n-3) in order.

Step 2

Why this answer is correct

The correct answer is D. सैंतालीस / (47). \(P_5=3+5+9+13+17=47\). In exams, add the numbers formed by (4n-3) in order.

Step 3

Exam Tip

\(P_5=3+5+9+13+17=47\) है। परीक्षा में (4n-3) से बनने वाली संख्याएँ क्रम से जोड़ें।

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Question 37/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(Q_1=2\), \(Q_2=5\) और \(Q_n=Q_{n-1}+2Q_{n-2}+n\) है, तो \(Q_5\) का मान क्या होगा?

If \(Q_1=2\), \(Q_2=5\), and \(Q_n=Q_{n-1}+2Q_{n-2}+n\), what is the value of \(Q_5\)?

Explanation opens after your attempt

Correct Answer

A. पचपन(55)

Step 1

Concept

\(Q_3=12\), \(Q_4=26\), and \(Q_5=55\). In exams, do not forget to double the second previous term.

Step 2

Why this answer is correct

The correct answer is A. पचपन / (55). \(Q_3=12\), \(Q_4=26\), and \(Q_5=55\). In exams, do not forget to double the second previous term.

Step 3

Exam Tip

\(Q_3=12\), \(Q_4=26\) और \(Q_5=55\) है। परीक्षा में दूसरे पिछले पद को दोगुना करना न भूलें।

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Question 38/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(R_1=1\) और \(R_n=R_{n-1}^2+n\) है, तो \(R_3\) का मान क्या होगा?

If \(R_1=1\) and \(R_n=R_{n-1}^2+n\), what is the value of \(R_3\)?

Explanation opens after your attempt

Correct Answer

C. बारह(12)

Step 1

Concept

\(R_2=3\) and \(R_3=12\). In exams, square the previous term and then add (n).

Step 2

Why this answer is correct

The correct answer is C. बारह / (12). \(R_2=3\) and \(R_3=12\). In exams, square the previous term and then add (n).

Step 3

Exam Tip

\(R_2=3\) और \(R_3=12\) है। परीक्षा में पिछले पद का वर्ग लेने के बाद (n) जोड़ें।

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Question 39/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम में \(S_1=100\) और \(S_n=S_{n-1}-n^2\) है। \(S_4\) का मान क्या होगा?

In a sequence, \(S_1=100\) and \(S_n=S_{n-1}-n^2\). What is the value of \(S_4\)?

Explanation opens after your attempt

Correct Answer

B. इकहत्तर(71)

Step 1

Concept

\(S_4=100-4-9-16=71\). In exams, subtract \(n^2\), do not add it.

Step 2

Why this answer is correct

The correct answer is B. इकहत्तर / (71). \(S_4=100-4-9-16=71\). In exams, subtract \(n^2\), do not add it.

Step 3

Exam Tip

\(S_4=100-4-9-16=71\) है। परीक्षा में \(n^2\) को घटाना है, जोड़ना नहीं।

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Question 40/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(T_1=2\) और (T_n=(n+1)T_{n-1}-n) है, तो \(T_4\) का मान क्या होगा?

If \(T_1=2\) and (T_n=(n+1)T_{n-1}-n), what is the value of \(T_4\)?

Explanation opens after your attempt

Correct Answer

D. इकसठ(61)

Step 1

Concept

\(T_2=4\), \(T_3=13\), and \(T_4=61\). In exams, multiply by ((n+1)) and subtract (n).

Step 2

Why this answer is correct

The correct answer is D. इकसठ / (61). \(T_2=4\), \(T_3=13\), and \(T_4=61\). In exams, multiply by ((n+1)) and subtract (n).

Step 3

Exam Tip

\(T_2=4\), \(T_3=13\) और \(T_4=61\) है। परीक्षा में ((n+1)) से गुणा करके (n) घटाएँ।

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Question 41/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

किसी अनुक्रम के पहले चार पद (5), (8), (14), (26) हैं और नियम \(a_n=2a_{n-1}-2\) है। \(a_5\) क्या होगा?

The first four terms of a sequence are (5), (8), (14), (26), and the rule is \(a_n=2a_{n-1}-2\). What is \(a_5\)?

Explanation opens after your attempt

Correct Answer

C. पचास(50)

Step 1

Concept

\(a_5=2\times 26-2=50\). In exams, apply the rule to the last given term.

Step 2

Why this answer is correct

The correct answer is C. पचास / (50). \(a_5=2\times 26-2=50\). In exams, apply the rule to the last given term.

Step 3

Exam Tip

\(a_5=2\times 26-2=50\) है। परीक्षा में दिए अंतिम पद पर नियम लगाएँ।

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Question 42/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(a_n=a_{n-1}+3n\) और \(a_4=31\) है, तो \(a_2\) का मान क्या होगा?

If \(a_n=a_{n-1}+3n\) and \(a_4=31\), what is the value of \(a_2\)?

Explanation opens after your attempt

Correct Answer

A. दस(10)

Step 1

Concept

\(a_4=a_2+9+12\), so \(a_2=10\). In exams, think backward for a middle term.

Step 2

Why this answer is correct

The correct answer is A. दस / (10). \(a_4=a_2+9+12\), so \(a_2=10\). In exams, think backward for a middle term.

Step 3

Exam Tip

\(a_4=a_2+9+12\), इसलिए \(a_2=10\) है। परीक्षा में बीच के पद के लिए उल्टी दिशा में सोचें।

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Question 43/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(b_n=2b_{n-1}+n\) और \(b_3=19\) है, तो \(b_1\) का मान क्या होगा?

If \(b_n=2b_{n-1}+n\) and \(b_3=19\), what is the value of \(b_1\)?

Explanation opens after your attempt

Correct Answer

B. तीन(3)

Step 1

Concept

\(b_3=4b_1+7\), so \(b_1=3\). In exams, expand the recursive rule up to the first term.

Step 2

Why this answer is correct

The correct answer is B. तीन / (3). \(b_3=4b_1+7\), so \(b_1=3\). In exams, expand the recursive rule up to the first term.

Step 3

Exam Tip

\(b_3=4b_1+7\), इसलिए \(b_1=3\) है। परीक्षा में पुनरावर्ती नियम को प्रथम पद तक फैलाएँ।

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Question 44/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(c_1=2\) और \(c_n=c_{n-1}+n^2\) है, तो कौन-सा कथन सही है?

If \(c_1=2\) and \(c_n=c_{n-1}+n^2\), which statement is correct?

Explanation opens after your attempt

Correct Answer

D. \(c_2=6\) और \(c_3=15\)\(c_2=6\) and \(c_3=15\)

Step 1

Concept

\(c_2=2+4=6\) and \(c_3=6+9=15\). In exams, add the new square for each term.

Step 2

Why this answer is correct

The correct answer is D. \(c_2=6\) और \(c_3=15\) / \(c_2=6\) and \(c_3=15\). \(c_2=2+4=6\) and \(c_3=6+9=15\). In exams, add the new square for each term.

Step 3

Exam Tip

\(c_2=2+4=6\) और \(c_3=6+9=15\) है। परीक्षा में प्रत्येक पद के लिए नया वर्ग जोड़ें।

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Question 45/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(d_1=1\) और \(d_n=d_{n-1}+3n\) है, तो \(d_n>40\) पहली बार किस (n) पर होगा?

If \(d_1=1\) and \(d_n=d_{n-1}+3n\), for which (n) will \(d_n>40\) first occur?

Explanation opens after your attempt

Correct Answer

C. पाँच(5)

Step 1

Concept

\(d_4=28\) and \(d_5=43\), so the condition is first satisfied at (n=5). In exams, choose the first term that crosses the limit.

Step 2

Why this answer is correct

The correct answer is C. पाँच / (5). \(d_4=28\) and \(d_5=43\), so the condition is first satisfied at (n=5). In exams, choose the first term that crosses the limit.

Step 3

Exam Tip

\(d_4=28\) और \(d_5=43\), इसलिए पहली बार (n=5) पर शर्त पूरी होती है। परीक्षा में सीमा पार करने वाला पहला पद चुनें।

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Question 46/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(e_1=3\) और \(e_n=2e_{n-1}+n\) है, तो \(e_5-e_4\) का मान क्या होगा?

If \(e_1=3\) and \(e_n=2e_{n-1}+n\), what is the value of \(e_5-e_4\)?

Explanation opens after your attempt

Correct Answer

A. सैंतालीस(47)

Step 1

Concept

\(e_4=42\) and \(e_5=89\), so the difference is (47). In exams, find both terms separately first.

Step 2

Why this answer is correct

The correct answer is A. सैंतालीस / (47). \(e_4=42\) and \(e_5=89\), so the difference is (47). In exams, find both terms separately first.

Step 3

Exam Tip

\(e_4=42\) और \(e_5=89\), इसलिए अंतर (47) है। परीक्षा में पहले दोनों पद अलग-अलग निकालें।

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Question 47/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(f_1=2\) और \(f_n=f_{n-1}+2n\) है, तो पहले चार पदों का योग क्या होगा?

If \(f_1=2\) and \(f_n=f_{n-1}+2n\), what is the sum of the first four terms?

Explanation opens after your attempt

Correct Answer

D. चालीस(40)

Step 1

Concept

The first four terms are (2), (6), (12), and (20), and their sum is (40). In exams, add all terms when the sum is asked.

Step 2

Why this answer is correct

The correct answer is D. चालीस / (40). The first four terms are (2), (6), (12), and (20), and their sum is (40). In exams, add all terms when the sum is asked.

Step 3

Exam Tip

पहले चार पद (2), (6), (12), (20) हैं और योग (40) है। परीक्षा में योग पूछने पर सभी पद जोड़ें।

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Question 48/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(g_1=1\) और \(g_n=3g_{n-1}-1\) है, तो \(g_4:g_3\) क्या होगा?

If \(g_1=1\) and \(g_n=3g_{n-1}-1\), what is \(g_4:g_3\)?

Explanation opens after your attempt

Correct Answer

B. (14:5)

Step 1

Concept

\(g_3=5\) and \(g_4=14\), so the ratio is (14:5). In exams, do not reverse the order of a ratio.

Step 2

Why this answer is correct

The correct answer is B. (14:5). \(g_3=5\) and \(g_4=14\), so the ratio is (14:5). In exams, do not reverse the order of a ratio.

Step 3

Exam Tip

\(g_3=5\) और \(g_4=14\), इसलिए अनुपात (14:5) है। परीक्षा में अनुपात का क्रम न बदलें।

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Question 49/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(h_1=2\), \(h_2=7\) और \(h_n=2h_{n-1}-h_{n-2}+3\) है, तो \(h_5\) का मान क्या होगा?

If \(h_1=2\), \(h_2=7\), and \(h_n=2h_{n-1}-h_{n-2}+3\), what is the value of \(h_5\)?

Explanation opens after your attempt

Correct Answer

C. चालीस(40)

Step 1

Concept

\(h_3=15\), \(h_4=26\), and \(h_5=40\). In exams, identify the term being subtracted correctly.

Step 2

Why this answer is correct

The correct answer is C. चालीस / (40). \(h_3=15\), \(h_4=26\), and \(h_5=40\). In exams, identify the term being subtracted correctly.

Step 3

Exam Tip

\(h_3=15\), \(h_4=26\) और \(h_5=40\) है। परीक्षा में घटाए जाने वाले पद को सही पहचानें।

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Question 50/50 Expert Mathematics Sequences and Progressions Recursive rule Class 9 Level 45

यदि \(p_1=1\) और \(p_n=p_{n-1}+n^2-n\) है, तो \(p_5\) का मान क्या होगा?

If \(p_1=1\) and \(p_n=p_{n-1}+n^2-n\), what is the value of \(p_5\)?

Explanation opens after your attempt

Correct Answer

A. इकतालीस(41)

Step 1

Concept

\(p_5=1+2+6+12+20=41\). In exams, simplify \(n^2-n\) and then add.

Step 2

Why this answer is correct

The correct answer is A. इकतालीस / (41). \(p_5=1+2+6+12+20=41\). In exams, simplify \(n^2-n\) and then add.

Step 3

Exam Tip

\(p_5=1+2+6+12+20=41\) है। परीक्षा में \(n^2-n\) को सरल करके जोड़ें।

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Class 9 Mathematics - Sequences and Progressions - Arithmetic Progression Expert Quiz

किसी अनुक्रम में \(a_1=3\) और \(a_n=2a_{n-1}+n+1\) है। \(a_4\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

किसी अनुक्रम में \(b_1=6\) और \(b_n=3b_{n-1}-n\) है। \(b_4\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

किसी अनुक्रम में \(c_1=1\), \(c_2=3\) और \(c_n=2c_{n-1}+c_{n-2}\) है। \(c_5\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(d_n=d_{n-1}+2n\) और \(d_4=25\) है, तो \(d_1\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

अनुक्रम (4), (9), (19), (39) के लिए कौन-सा पुनरावर्ती नियम सही है?

Concept

Why this answer is correct

Exam Tip

यदि \(f_1=10\) और \(f_n=f_{n-1}-n\) है, तो पहला ऋणात्मक पद कौन-सा होगा?

Concept

Why this answer is correct

Exam Tip

किसी अनुक्रम में \(g_1=2\) और \(g_n=g_{n-1}+2n-1\) है। \(g_5\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(h_1=3\) और \(h_n=n h_{n-1}\) है, तो \(h_4\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

किसी अनुक्रम में \(j_1=1\) और \(j_n=j_{n-1}+n^2\) है। \(j_4\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(k_1=64\) और \(k_n=\frac{k_{n-1}}{2}+n\) है, तो \(k_4\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

किसी अनुक्रम में \(m_1=2\) और \(m_n=m_{n-1}+3n\) है। \(m_4\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(n_1=5\) और \(n_n=2n_{n-1}-n^2\) है, तो \(n_4\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(r_1=1\), \(r_2=2\) और \(r_n=r_{n-1}+3r_{n-2}\) है, तो \(r_5\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

किसी अनुक्रम में \(s_1=3\) और (s_n=s_{n-1}+(-1)^n n) है। \(s_5\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(t_1=x\), \(t_n=t_{n-1}+n\) और \(t_5=24\) है, तो (x) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

अनुक्रम (2), (6), (18), (54) के लिए सही पुनरावर्ती नियम कौन-सा है?

Concept

Why this answer is correct

Exam Tip

यदि \(v_1=4\) और \(v_n=2v_{n-1}-1\) है, तो \(v_5\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

किसी अनुक्रम में \(w_1=0\) और \(w_n=w_{n-1}+2^{n-1}\) है। \(w_5\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(x_1=1\) और \(x_n=2x_{n-1}+n^2\) है, तो \(x_3\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

किसी अनुक्रम में \(y_1=7\) और (y_n=y_{n-1}+(n-1)2) है। \(y_5\) का मान क्या होगा?

Concept

Why this answer is correct

किसी अनुक्रम में \(y_1=7\) और (y_n=y_{n-1}+(n-1)²) है। \(y_5\) का मान क्या होगा?