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
5701	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	2
5702	Find $ S_{ 81 } $ ( sum of first $ 81 $ terms ) of arithmetic progression if $ a_1 = \frac{ 7 }{ 2 } ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $.	2
5703	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	2
5704	Find $ S_{ 35 } $ ( sum of first $ 35 $ terms ) of arithmetic progression if $ a_1 = 33 ~~ \text{and} ~~ d = 2 $.	2
5705	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 43 ~~ \text{and} ~~ d = 3 $.	2
5706	Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = 43 ~~ \text{and} ~~ d = 3 $.	2
5707	Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 7 $.	2
5708	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 6 $.	2
5709	$$ a_1 = 3 ~~,~~ d = 100 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
5710	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $.	2
5711	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	2
5712	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 3 $.	2
5713	Find $ a_{ 77 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	2
5714	Find $ S_{ 35 } $ ( sum of first $ 35 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
5715	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = -24 ~~ \text{and} ~~ d = 10 $.	2
5716	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = \left( -24 \right) $.	2
5717	Find $ a_{ 77 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 44 $.	2
5718	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 11 $.	2
5719	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 11 $.	2
5720	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 11 $.	2
5721	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = \frac{ 9 }{ 2 } ~~ \text{and} ~~ d = 0 $.	2
5722	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = -17 ~~ \text{and} ~~ d = 5 $.	2
5723	Find $ S_{ 350 } $ ( sum of first $ 350 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	2
5724	Find $ S_{ 160 } $ ( sum of first $ 160 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	2
5725	Find $ S_{ 120 } $ ( sum of first $ 120 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	2
5726	Find $ S_{ 90 } $ ( sum of first $ 90 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	2
5727	Find $ a_1 $ (first term of arithmetic progression) if $ d = 2 ~~ \text{and} ~~ a_{ 14 } = \frac{ 753 }{ 50 } $.	2
5728	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 2 $.	2
5729	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $.	2
5730	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 0 $.	2
5731	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 16 $.	2
5732	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 21 $.	2
5733	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = 360 ~~ \text{and} ~~ d = -24 $.	2
5734	Find $ S_{ 2 } $ ( sum of first $ 2 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ d = -\frac{ 2 }{ 3 } $.	2
5735	Find $ S_{ 60 } $ ( sum of first $ 60 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 7 $.	2
5736	$$ a_1 = 6 ~,~ d = 13 ~,~ a_n = 786 ~,~ n = ? $$	2
5737	Find $ S_{ 61 } $ ( sum of first $ 61 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 13 $.	2
5738	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 1 $.	2
5739	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 1 $.	2
5740	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 6 $.	2
5741	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 15 $.	2
5742	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 6 $.	2
5743	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 2 $.	2
5744	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = \frac{ 7 }{ 10 } ~~ \text{and} ~~ d = \left( -\frac{ 2 }{ 5 } \right) $.	2
5745	Find $ S_{ 85 } $ ( sum of first $ 85 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
5746	Find $ a_{ 37 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	2
5747	Find common difference $ d $ of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ a_{ 9 } = 4 $.	2
5748	Find common difference $ d $ of arithmetic progression if $ a_1 = 46 ~~ \text{and} ~~ a_{ 32 } = 78 $.	2
5749	Find $ S_{ 89 } $ ( sum of first $ 89 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ d = \frac{ 1 }{ 100 } $.	2
5750	$$ a_1 = 40 ~,~ a_n = 12 ~,~ S_n = 744 ~,~ n = ? $$	2