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
4551	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 4 $.	2
4552	Find $ a_{ 38 } $ of an arithmetic progression if $ a_1 = 355 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
4553	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 7 $.	2
4554	Find $ a_{ 92 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 4 $.	2
4555	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 8 $.	2
4556	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
4557	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -14 ~~ \text{and} ~~ d = 0 $.	2
4558	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 6 $.	2
4559	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 4 $.	2
4560	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $.	2
4561	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 13 }{ 5 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
4562	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 7 $.	2
4563	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 280 ~~ \text{and} ~~ d = \left( -23 \right) $.	2
4564	Find $ S_{ 1100 } $ ( sum of first $ 1100 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 0 $.	2
4565	Find $ S_{ 3 } $ ( sum of first $ 3 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = -4 $.	2
4566	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = \frac{ 24 }{ 5 } ~~ \text{and} ~~ d = \left( -2 \right) $.	2
4567	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = \frac{ 22 }{ 3 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
4568	Find $ S_{ 199 } $ ( sum of first $ 199 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	2
4569	Find $ a_{ 90 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	2
4570	Find $ S_{ 90 } $ ( sum of first $ 90 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	2
4571	$$ a_1 = 0 ~,~ d = 4 ~,~ S_n = 79600 ~,~ n = ? $$	2
4572	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = \left( -6 \right) $.	2
4573	Find $ a_{ 220 } $ of an arithmetic progression if $ a_1 = 143 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
4574	Find $ a_1 $ (first term of arithmetic progression) if $ d = 1 ~~ \text{and} ~~ a_{ 6 } = 55 $.	2
4575	Find $ S_{ 57 } $ ( sum of first $ 57 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 8 $.	2
4576	Find $ a_{ 1000 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 5 $.	2
4577	Find $ S_{ 1000 } $ ( sum of first $ 1000 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 5 $.	2
4578	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = \frac{ 23 }{ 100 } ~~ \text{and} ~~ d = \frac{ 1 }{ 10 } $.	2
4579	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 100 $.	2
4580	Find $ a_1 $ (first term of arithmetic progression) if $ d = 1 ~~ \text{and} ~~ a_{ 8 } = 14 $.	2
4581	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 100 $.	2
4582	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1000 $.	2
4583	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1000 $.	2
4584	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = -22 $.	2
4585	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 4 } ~~ \text{and} ~~ d = \frac{ 1 }{ 8 } $.	2
4586	Find $ S_{ 80 } $ ( sum of first $ 80 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 6 $.	2
4587	Find $ S_{ 85 } $ ( sum of first $ 85 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 5 $.	2
4588	Find $ S_{ 250 } $ ( sum of first $ 250 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	2
4589	Find $ a_{ 46 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 8 $.	2
4590	Find $ a_{ 78 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 4 $.	2
4591	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 9 $.	2
4592	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 5 $.	2
4593	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 6 $.	2
4594	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 7 $.	2
4595	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = \frac{ 13 }{ 5 } ~~ \text{and} ~~ d = \frac{ 9 }{ 5 } $.	2
4596	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
4597	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
4598	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 25 $.	2
4599	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 56 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
4600	Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = 77 ~~ \text{and} ~~ d = \left( -4 \right) $.	2