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Mathematics Finding the $n$th term of an AP MCQ Questions for Class 10

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Finding the $n$th term of an AP Practice Questions

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Question 21/600 Easy Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि समांतर श्रेढ़ी में (a=14) और (d=6) है, तो (19)वाँ पद ज्ञात करें।

If an AP has (a=14) and (d=6), find the (19)th term.

Explanation opens after your attempt
Correct Answer

C. (122)

Step 1

Concept

\(a_{19}=14+18\times6=122\). Multiply by (n-1) and then add the first term.

Step 2

Why this answer is correct

The correct answer is C. (122). \(a_{19}=14+18\times6=122\). Multiply by (n-1) and then add the first term.

Step 3

Exam Tip

\(a_{19}=14+18\times6=122\)। (n-1) को गुणा करके फिर प्रथम पद जोड़ें।

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Question 22/600 Easy Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समांतर श्रेढ़ी \(4,4,4,4,\ldots\) का (50)वाँ पद क्या है?

What is the (50)th term of the AP \(4,4,4,4,\ldots\)?

Explanation opens after your attempt
Correct Answer

D. (4)

Step 1

Concept

Here (d=0), so every term remains (4). In a constant AP, \(a_n=a\).

Step 2

Why this answer is correct

The correct answer is D. (4). Here (d=0), so every term remains (4). In a constant AP, \(a_n=a\).

Step 3

Exam Tip

यहाँ (d=0) है, इसलिए हर पद (4) रहेगा। समान पदों वाली श्रेढ़ी में \(a_n=a\) होता है।

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Question 23/600 Easy Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समांतर श्रेढ़ी \(6,10,14,18,\ldots\) का (31)वाँ पद क्या होगा?

What will be the (31)st term of the AP \(6,10,14,18,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. (126)

Step 1

Concept

Here (a=6), (d=4), so \(a_{31}=6+30\times4=126\). For the (31)st term, add (30) differences.

Step 2

Why this answer is correct

The correct answer is A. (126). Here (a=6), (d=4), so \(a_{31}=6+30\times4=126\). For the (31)st term, add (30) differences.

Step 3

Exam Tip

यहाँ (a=6), (d=4) है, इसलिए \(a_{31}=6+30\times4=126\)। (31)वें पद के लिए (30) अंतर जोड़ें।

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Question 24/600 Easy Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समांतर श्रेढ़ी \(9,5,1,-3,\ldots\) का (8)वाँ पद ज्ञात कीजिए।

Find the (8)th term of the AP \(9,5,1,-3,\ldots\).

Explanation opens after your attempt
Correct Answer

B. (-19)

Step 1

Concept

Here (d=-4), so (a_8=9+7(-4)=-19). Brackets are useful with negative (d).

Step 2

Why this answer is correct

The correct answer is B. (-19). Here (d=-4), so (a_8=9+7(-4)=-19). Brackets are useful with negative (d).

Step 3

Exam Tip

यहाँ (d=-4) है, इसलिए (a_8=9+7(-4)=-19)। ऋणात्मक (d) के साथ कोष्ठक उपयोगी होते हैं।

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Question 25/600 Easy Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक समांतर श्रेढ़ी में (a=3) और (d=10) है। (13)वाँ पद क्या होगा?

In an AP, (a=3) and (d=10). What will be the (13)th term?

Explanation opens after your attempt
Correct Answer

C. (123)

Step 1

Concept

\(a_{13}=3+12\times10=123\). It is easy to find (12d) first and then add (a).

Step 2

Why this answer is correct

The correct answer is C. (123). \(a_{13}=3+12\times10=123\). It is easy to find (12d) first and then add (a).

Step 3

Exam Tip

\(a_{13}=3+12\times10=123\)। पहले (12d) निकालकर (a) जोड़ना आसान है।

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Question 26/600 Easy Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समांतर श्रेढ़ी \(11,16,21,26,\ldots\) का (9)वाँ पद क्या है?

What is the (9)th term of the AP \(11,16,21,26,\ldots\)?

Explanation opens after your attempt
Correct Answer

D. (51)

Step 1

Concept

Here (a=11), (d=5), so \(a_9=11+8\times5=51\). One less than the term number is added as differences.

Step 2

Why this answer is correct

The correct answer is D. (51). Here (a=11), (d=5), so \(a_9=11+8\times5=51\). One less than the term number is added as differences.

Step 3

Exam Tip

यहाँ (a=11), (d=5) है, इसलिए \(a_9=11+8\times5=51\)। पद संख्या से एक कम अंतर जुड़ता है।

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Question 27/600 Easy Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

किसी समांतर श्रेढ़ी का (n)वाँ पद \(a_n=2n+3\) है। (18)वाँ पद क्या होगा?

The (n)th term of an AP is \(a_n=2n+3\). What will be the (18)th term?

Explanation opens after your attempt
Correct Answer

A. (39)

Step 1

Concept

Putting (n=18), \(a_{18}=2\times18+3=39\). Substitute the term number directly in the given \(a_n\).

Step 2

Why this answer is correct

The correct answer is A. (39). Putting (n=18), \(a_{18}=2\times18+3=39\). Substitute the term number directly in the given \(a_n\).

Step 3

Exam Tip

(n=18) रखने पर \(a_{18}=2\times18+3=39\)। दिए गए \(a_n\) में सीधे पद संख्या रखें।

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Question 28/600 Easy Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_n=5n-1\) हो, तो इस समांतर श्रेढ़ी का (20)वाँ पद क्या है?

If \(a_n=5n-1\), what is the (20)th term of this AP?

Explanation opens after your attempt
Correct Answer

B. (99)

Step 1

Concept

\(a_{20}=5\times20-1=99\). When \(a_n\) is given, put the value of (n) in it.

Step 2

Why this answer is correct

The correct answer is B. (99). \(a_{20}=5\times20-1=99\). When \(a_n\) is given, put the value of (n) in it.

Step 3

Exam Tip

\(a_{20}=5\times20-1=99\)। जब \(a_n\) दिया हो, तो सूत्र में (n) का मान रखें।

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Question 29/600 Easy Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समांतर श्रेढ़ी का सामान्य पद \(a_n=7n+2\) है। (11)वाँ पद ज्ञात कीजिए।

The general term of an AP is \(a_n=7n+2\). Find the (11)th term.

Explanation opens after your attempt
Correct Answer

C. (79)

Step 1

Concept

\(a_{11}=7\times11+2=79\). The main step is substituting the correct term number in the general term.

Step 2

Why this answer is correct

The correct answer is C. (79). \(a_{11}=7\times11+2=79\). The main step is substituting the correct term number in the general term.

Step 3

Exam Tip

\(a_{11}=7\times11+2=79\)। सामान्य पद में सही पद संख्या रखना ही मुख्य कदम है।

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Question 30/600 Easy Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_n=30-3n\) है, तो (6)वाँ पद क्या होगा?

If \(a_n=30-3n\), what will be the (6)th term?

Explanation opens after your attempt
Correct Answer

D. (12)

Step 1

Concept

\(a_6=30-3\times6=12\). Be careful with subtraction in a decreasing general term.

Step 2

Why this answer is correct

The correct answer is D. (12). \(a_6=30-3\times6=12\). Be careful with subtraction in a decreasing general term.

Step 3

Exam Tip

\(a_6=30-3\times6=12\)। घटते हुए सामान्य पद में घटाव सावधानी से करें।

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