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
4601	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 40 ~~ \text{and} ~~ d = -8 $.	2
4602	$$ a_1 = 21 ~~,~~ d = -4 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
4603	Find $ a_1 $ (first term of arithmetic progression) if $ d = -4 ~~ \text{and} ~~ a_{ 15 } = 21 $.	2
4604	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 7 $.	2
4605	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 12 $.	2
4606	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \left( -12 \right) $.	2
4607	Find $ a_{ 99 } $ of an arithmetic progression if $ a_1 = -56 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
4608	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 4 $.	2
4609	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = \frac{ 15 }{ 2 } $.	2
4610	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $.	2
4611	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 31 ~~ \text{and} ~~ d = 9 $.	2
4612	Find $ S_{ 110 } $ ( sum of first $ 110 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 2 $.	2
4613	Find $ S_{ 110 } $ ( sum of first $ 110 $ terms ) of arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 2 $.	2
4614	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = -6 $.	2
4615	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 6 $.	2
4616	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 8 $.	2
4617	Find $ S_{ 49 } $ ( sum of first $ 49 $ terms ) of arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 1 $.	2
4618	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $.	2
4619	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 6 $.	2
4620	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 3 $.	2
4621	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 7 $.	2
4622	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 4 $.	2
4623	Find $ a_{ 41 } $ of an arithmetic progression if $ a_1 = -96 ~~ \text{and} ~~ d = \left( -18 \right) $.	2
4624	Find $ S_{ 41 } $ ( sum of first $ 41 $ terms ) of arithmetic progression if $ a_1 = -96 ~~ \text{and} ~~ d = -18 $.	2
4625	Find common difference $ d $ of arithmetic progression if $ a_1 = \frac{ 7 }{ 4 } ~~ \text{and} ~~ a_{ 4 } = \frac{ 33 }{ 4 } $.	2
4626	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = \frac{ 29 }{ 4 } ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $.	2
4627	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
4628	$$ a_1 = 3 ~,~ d = 5 ~,~ a_n = 193 ~,~ n = ? $$	2
4629	$$ a_1 = 3 ~,~ d = 4 ~,~ a_n = 55 ~,~ n = ? $$	2
4630	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \left( -6 \right) $.	2
4631	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 3 $.	2
4632	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $.	2
4633	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 67 ~~ \text{and} ~~ d = 16 $.	2
4634	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 67 ~~ \text{and} ~~ d = 16 $.	2
4635	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 67 ~~ \text{and} ~~ d = 16 $.	2
4636	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -90 ~~ \text{and} ~~ d = 1 $.	2
4637	Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 8 $.	2
4638	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 86 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
4639	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = 3 $.	2
4640	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = 5 $.	2
4641	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	2
4642	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 4 $.	2
4643	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
4644	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 5 $.	2
4645	Find $ a_1 $ (first term of arithmetic progression) if $ d = 3 ~~ \text{and} ~~ a_{ 15 } = 50 $.	2
4646	Find common difference $ d $ of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ a_{ 5 } = 10 $.	2
4647	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = -100 ~~ \text{and} ~~ d = 12 $.	2
4648	Find $ a_1 $ (first term of arithmetic progression) if $ d = \frac{ 3 }{ 4 } ~~ \text{and} ~~ a_{ 21 } = \frac{ 37 }{ 2 } $.	2
4649	Find $ S_{ 65 } $ ( sum of first $ 65 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ d = \frac{ 3 }{ 10 } $.	2
4650	Find $ S_{ 500 } $ ( sum of first $ 500 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2