Arithmetic sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Arithmetic sequences.

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ID	Problem	Count
5601	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 6 $.	2
5602	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 6 $.	2
5603	Find $ a_{ 58 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 6 $.	2
5604	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -\frac{ 1 }{ 3 } ~~ \text{and} ~~ d = \frac{ 3 }{ 4 } $.	2
5605	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 9 $.	2
5606	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 4000 ~~ \text{and} ~~ d = 800 $.	2
5607	Find $ S_{ 22 } $ ( sum of first $ 22 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 4 $.	2
5608	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 11 $.	2
5609	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 85 ~~ \text{and} ~~ d = 0 $.	2
5610	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 26 $.	2
5611	Find $ a_{ 267 } $ of an arithmetic progression if $ a_1 = 69 ~~ \text{and} ~~ d = 125 $.	2
5612	$$ a_1 = 0 ~,~ d = 13500 ~,~ S_n = 350000 ~,~ n = ? $$	2
5613	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ d = \frac{ 1 }{ 6 } $.	2
5614	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = -20 ~~ \text{and} ~~ d = 3 $.	2
5615	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = -4 $.	2
5616	Find $ S_{ 3 } $ ( sum of first $ 3 $ terms ) of arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = \frac{ 375 }{ 2 } $.	2
5617	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = \frac{ 375 }{ 2 } $.	2
5618	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = \frac{ 375 }{ 2 } $.	2
5619	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = -20 ~~ \text{and} ~~ d = 3 $.	2
5620	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 4 $.	2
5621	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 2 $.	2
5622	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \frac{ 1 }{ 50 } $.	2
5623	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \frac{ 1 }{ 10 } $.	2
5624	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
5625	Find $ S_{ 104 } $ ( sum of first $ 104 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 250 $.	2
5626	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -12 \right) $.	2
5627	Find $ a_{ 102 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $.	2
5628	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 10 $.	2
5629	Find $ a_{ 125 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
5630	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 6 $.	2
5631	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 8 $.	2
5632	Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 6 $.	2
5633	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 5000 ~~ \text{and} ~~ d = 1000 $.	2
5634	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
5635	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 4 } \right) $.	2
5636	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = -32 ~~ \text{and} ~~ d = \left( -100 \right) $.	2
5637	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = -27 ~~ \text{and} ~~ d = 6 $.	2
5638	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 9 $.	2
5639	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 9 $.	2
5640	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = -5 $.	2
5641	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 7 $.	2
5642	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 10 $.	2
5643	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ d = \frac{ 8 }{ 5 } $.	2
5644	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = \left( -9 \right) $.	2
5645	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = -6 $.	2
5646	$$ a_1 = 156 ~,~ d = -2 ~,~ a_n = 92 ~,~ n = ? $$	2
5647	Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 156 ~~ \text{and} ~~ d = -2 $.	2
5648	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = 8 $.	2
5649	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 137 ~~ \text{and} ~~ d = 8 $.	2
5650	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 89 ~~ \text{and} ~~ d = 6 $.	2