nth_term se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
254 questions tagged with nth_term.
If (a=25), (d=-2), and (n=17), what is \(a_n\)?
B. (-7)
(a_{17}=25+16(-2)=-7)। ऋणात्मक सार्व अंतर को सही से गुणा करें। / (a_{17}=25+16(-2)=-7). Multiply the negative common difference carefully.
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What is the (25)th term of the AP \(3,3,3,3,\ldots\)?
B. (3)
यहाँ (d=0) है इसलिए हर पद (3) रहेगा। समान पदों वाली एपी में \(a_n=a\) होता है। / Here (d=0), so every term remains (3). In a constant AP, \(a_n=a\).
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Find the (10)th term of the AP \(\frac{1}{2},1,\frac{3}{2},2,\ldots\).
C. (5)
यहाँ \(a=\frac{1}{2}\) और \(d=\frac{1}{2}\) है इसलिए \(a_{10}=5\)। भिन्नों में हर समान रखकर जोड़ें। / Here \(a=\frac{1}{2}\) and \(d=\frac{1}{2}\), so \(a_{10}=5\). Use a common denominator while adding fractions.
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What is the (21)st term of the AP \(0,5,10,15,\ldots\)?
B. (100)
यहाँ (a=0) और (d=5) है इसलिए \(a_{21}=0+20\times5=100\)। प्रथम पद (0) हो सकता है। / Here (a=0) and (d=5), so \(a_{21}=0+20\times5=100\). The first term can be (0).
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If the AP is \(4,9,14,19,\ldots\), what is the (16)th term?
C. (79)
यहाँ (d=5) है इसलिए \(a_{16}=4+15\times5=79\)। (16)वें पद के लिए (15d) जोड़ें। / Here (d=5), so \(a_{16}=4+15\times5=79\). For the (16)th term, add (15d).
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Find the (13)th term of the AP \(50,47,44,41,\ldots\).
B. (14)
यहाँ (d=-3) है इसलिए (a_{13}=50+12(-3)=14)। घटती एपी में पद छोटे होते जाते हैं। / Here (d=-3), so (a_{13}=50+12(-3)=14). In a decreasing AP, terms keep getting smaller.
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What is the (18)th term in the AP \(11,14,17,20,\ldots\)?
B. (62)
यहाँ (d=3) है इसलिए \(a_{18}=11+17\times3=62\)। लंबी पद संख्या में भी (n-1) का उपयोग करें। / Here (d=3), so \(a_{18}=11+17\times3=62\). Use (n-1) even for a larger term number.
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If (a=3) and (d=9), what is the (7)th term?
C. (57)
\(a_7=3+6\times9=57\)। (n) की जगह (7) रखने पर (6d) जुड़ता है। / \(a_7=3+6\times9=57\). When (n=7), (6d) is added.
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What is the (12)th term of the AP \(100,90,80,70,\ldots\)?
B. (-10)
यहाँ (d=-10) है इसलिए (a_{12}=100+11(-10)=-10)। बड़े अंतर में भी वही सूत्र लगता है। / Here (d=-10), so (a_{12}=100+11(-10)=-10). The same formula works for large differences too.
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Find the (10)th term of the AP \(6,13,20,27,\ldots\).
B. (69)
यहाँ (d=7) है इसलिए \(a_{10}=6+9\times7=69\)। (10)वें पद के लिए (9d) जोड़ें। / Here (d=7), so \(a_{10}=6+9\times7=69\). For the (10)th term, add (9d).
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If the first term of an AP is (15) and the common difference is (-4), what is the (8)th term?
A. (-13)
(a_8=15+7(-4)=-13)। ऋणात्मक (d) को कोष्ठक में लिखना उपयोगी है। / (a_8=15+7(-4)=-13). Writing negative (d) in brackets is useful.
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What is the (14)th term in the AP \(-10,-7,-4,-1,\ldots\)?
D. (29)
यहाँ (d=3) है इसलिए \(a_{14}=-10+13\times3=29\)। ऋणात्मक (a) के साथ जोड़ सही करें। / Here (d=3), so \(a_{14}=-10+13\times3=29\). Add carefully with a negative (a).
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What is the (9)th term of the AP \(13,17,21,25,\ldots\)?
C. (45)
यहाँ (d=4) है इसलिए \(a_9=13+8\times4=45\)। पहले दो पदों का अंतर जांचें। / Here (d=4), so \(a_9=13+8\times4=45\). Check the difference between the first two terms.
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If \(a_1=8\) and (d=2), what is the (20)th term?
B. (46)
\(a_{20}=8+19\times2=46\)। \(a_1\) ही प्रथम पद होता है। / \(a_{20}=8+19\times2=46\). \(a_1\) is the first term.
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Find the (6)th term of the AP \(30,25,20,15,\ldots\).
B. (5)
यहाँ (d=-5) है इसलिए (a_6=30+5(-5)=5)। घटते क्रम में सार्व अंतर ऋणात्मक लें। / Here (d=-5), so (a_6=30+5(-5)=5). Take the common difference as negative in decreasing order.
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What is the (15)th term of the AP \(1,4,7,10,\ldots\)?
C. (43)
यहाँ (a=1) और (d=3) है इसलिए \(a_{15}=1+14\times3=43\)। क्रमांक से (1) कम लेना जरूरी है। / Here (a=1) and (d=3), so \(a_{15}=1+14\times3=43\). Taking one less than the term number is necessary.
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If an AP has (a=4) and (d=7), what is its (5)th term?
C. (32)
\(a_5=4+4\times7=32\)। (5)वें पद के लिए (4d) जोड़ते हैं। / \(a_5=4+4\times7=32\). For the (5)th term, add (4d).
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What is the (11)th term in the AP \(9,6,3,0,\ldots\)?
B. (-21)
यहाँ (d=-3) है इसलिए (a_{11}=9+10(-3)=-21)। ऋण चिह्न को सही रखें। / Here (d=-3), so (a_{11}=9+10(-3)=-21). Keep the negative sign correct.
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Find the (7)th term of the AP \(-3,1,5,9,\ldots\).
C. (21)
यहाँ (a=-3) और (d=4) है इसलिए \(a_7=-3+6\times4=21\)। ऋणात्मक प्रथम पद से सावधानी रखें। / Here (a=-3) and (d=4), so \(a_7=-3+6\times4=21\). Be careful with a negative first term.
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What is the (9)th term of the AP \(20,18,16,14,\ldots\)?
B. (4)
यहाँ (d=-2) है इसलिए (a_9=20+8(-2)=4)। घटती एपी में (d) ऋणात्मक होता है। / Here (d=-2), so (a_9=20+8(-2)=4). In a decreasing AP, (d) is negative.
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If (a=12), (d=5), and (n=6), what is the value of \(a_n\)?
C. (37)
(a_n=12+(6-1)\times5=37)। सूत्र में सीधे मान रखने से गलती कम होती है। / (a_n=12+(6-1)\times5=37). Substituting values directly reduces mistakes.
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What is the (10)th term in the AP \(7,11,15,19,\ldots\)?
C. (43)
यहाँ (d=4) है इसलिए \(a_{10}=7+9\times4=43\)। पद संख्या से (1) घटाकर गुणा करें। / Here (d=4), so \(a_{10}=7+9\times4=43\). Multiply by one less than the term number.
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Find the (12)th term of the AP \(2,6,10,14,\ldots\).
B. (46)
यहाँ (a=2) और (d=4) है इसलिए \(a_{12}=2+11\times4=46\)। पहले सार्व अंतर निकालें। / Here (a=2) and (d=4), so \(a_{12}=2+11\times4=46\). First find the common difference.
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If the first term of an AP is (5) and common difference is (3), what is the (8)th term?
C. (26)
सूत्र (a_n=a+(n-1)d) लगाएं तो \(5+7\times3=26\)। परीक्षा में (n-1) लेना न भूलें। / Using (a_n=a+(n-1)d), \(5+7\times3=26\). In exams, do not forget (n-1).
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What is the (11)th term of the AP \(200,180,160,140,\ldots\)?
D. (0)
यहाँ (d=-20) है, इसलिए (a_{11}=200+10(-20)=0)। घटती श्रेढ़ी में पद शून्य भी हो सकता है। / Here (d=-20), so (a_{11}=200+10(-20)=0). In a decreasing AP, a term can also become zero.
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C. (44) सेंटीमीटर(44) cm
यहाँ (a=12), (d=4) है, इसलिए \(a_9=12+8\times4=44\)। समय आधारित प्रश्नों में पहला सप्ताह प्रथम पद होता है। / Here (a=12), (d=4), so \(a_9=12+8\times4=44\). In time-based questions, the first week is the first term.
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What will be the (51)st term of the AP \(1,3,5,7,\ldots\)?
B. (101)
यहाँ (a=1), (d=2) है, इसलिए \(a_{51}=1+50\times2=101\)। विषम संख्याओं वाली श्रेढ़ी में भी सूत्र सबसे सुरक्षित है। / Here (a=1), (d=2), so \(a_{51}=1+50\times2=101\). Even for odd numbers, the formula is the safest method.
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If (a=5) and (d=-1), find the (20)th term of the AP.
B. (-14)
(a_{20}=5+19(-1)=-14)। (d=-1) होने पर हर पद एक कम होता है। / (a_{20}=5+19(-1)=-14). When (d=-1), each term decreases by one.
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If \(a_n=4n+6\), what will be the (25)th term?
A. (106)
\(a_{25}=4\times25+6=106\)। दिए गए सामान्य पद में (n=25) रखें। / \(a_{25}=4\times25+6=106\). Put (n=25) in the given general term.
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What is the (18)th term of the AP \(16,24,32,40,\ldots\)?
D. (152)
यहाँ (a=16), (d=8) है, इसलिए \(a_{18}=16+17\times8=152\)। पहले पद को भी उत्तर में शामिल करना न भूलें। / Here (a=16), (d=8), so \(a_{18}=16+17\times8=152\). Do not forget to include the first term.
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