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
5301	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	2
5302	$$ a_{ 6 } = 17 ~~,~~ S_{ 10 } = 162 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
5303	Find $ a_1 $ (first term of arithmetic progression) if $ d = 4 ~~ \text{and} ~~ S_{ 14 } = 784 $.	2
5304	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = \frac{ 7 }{ 2 } ~~ \text{and} ~~ d = \frac{ 7 }{ 2 } $.	2
5305	$$ a_1 = 1 ~,~ d = 2 ~,~ S_n = 500 ~,~ n = ? $$	2
5306	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	2
5307	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
5308	$$ a_1 = 1 ~,~ d = \frac{ 5 }{ 2 } ~,~ a_n = 6 ~,~ n = ? $$	2
5309	Find $ a_{ 74 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
5310	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 79 $.	2
5311	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 33 $.	2
5312	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -32 ~~ \text{and} ~~ d = \left( -10 \right) $.	2
5313	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -32 ~~ \text{and} ~~ d = -10 $.	2
5314	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \left( -11 \right) $.	2
5315	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = \left( -11 \right) $.	2
5316	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	2
5317	Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = -32 ~~ \text{and} ~~ d = 4 $.	2
5318	Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = -32 ~~ \text{and} ~~ d = 3 $.	2
5319	Find $ a_{ 9000 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 0 $.	2
5320	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 10 $.	2
5321	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ d = \frac{ 2 }{ 5 } $.	2
5322	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
5323	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
5324	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 200 $.	2
5325	Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = 10 $.	2
5326	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 77 }{ 2 } $.	2
5327	Find $ a_{ 56 } $ of an arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = 11 $.	2
5328	Find $ S_{ 27 } $ ( sum of first $ 27 $ terms ) of arithmetic progression if $ a_1 = 83 ~~ \text{and} ~~ d = -3 $.	2
5329	Find $ S_{ 36 } $ ( sum of first $ 36 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	2
5330	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
5331	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = \frac{ 65 }{ 4 } ~~ \text{and} ~~ d = \frac{ 13 }{ 4 } $.	2
5332	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 13 $.	2
5333	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \left( -\frac{ 22 }{ 5 } \right) $.	2
5334	Find $ S_{ 38 } $ ( sum of first $ 38 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $.	2
5335	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 7 $.	2
5336	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ d = 0 $.	2
5337	Find $ S_{ 64 } $ ( sum of first $ 64 $ terms ) of arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 85 $.	2
5338	$$ a_1 = 1 ~~,~~ d = 1 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
5339	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	2
5340	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 2 $.	2
5341	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
5342	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
5343	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $.	2
5344	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	2
5345	Find $ a_{ 63 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 7 $.	2
5346	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = 9 $.	2
5347	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = 9 $.	2
5348	Find $ a_{ 581 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 12 $.	2
5349	Find $ a_1 $ (first term of arithmetic progression) if $ d = -\frac{ 3 }{ 10 } ~~ \text{and} ~~ a_{ 7 } = 2 $.	2
5350	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2