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
4301	$$ a_1 = 1 ~,~ a_n = 19 ~,~ S_n = 100 ~,~ n = ? $$	2
4302	$$ a_{ 16 } = 15 ~~,~~ S_{ 16 } = -120 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
4303	$$ a_{ 15 } = \frac{ 29 }{ 5 } ~~,~~ S_{ 15 } = 45 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
4304	$$ a_{ 34 } = -85 ~~,~~ S_{ 34 } = -1207 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
4305	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -\frac{ 51 }{ 10 } \right) $.	2
4306	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
4307	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -6 \right) $.	2
4308	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -\frac{ 11 }{ 2 } \right) $.	2
4309	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -\frac{ 11 }{ 2 } \right) $.	2
4310	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -\frac{ 11 }{ 2 } \right) $.	2
4311	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -\frac{ 11 }{ 2 } \right) $.	2
4312	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = \left( -\frac{ 31 }{ 10 } \right) $.	2
4313	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
4314	Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 2 $.	2
4315	Find $ a_{ 174 } $ of an arithmetic progression if $ a_1 = 33 ~~ \text{and} ~~ d = \left( -6 \right) $.	2
4316	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 51 }{ 10 } $.	2
4317	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $.	2
4318	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 26 }{ 5 } $.	2
4319	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $.	2
4320	Find $ S_{ 63 } $ ( sum of first $ 63 $ terms ) of arithmetic progression if $ a_1 = -19 ~~ \text{and} ~~ d = 6 $.	2
4321	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = 2 $.	2
4322	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 50 $.	2
4323	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 50 $.	2
4324	$$ a_1 = 19 ~,~ d = 24 ~,~ a_n = 633 ~,~ n = ? $$	2
4325	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = -98 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
4326	Find $ a_{ 432 } $ of an arithmetic progression if $ a_1 = 3984 ~~ \text{and} ~~ d = 9 $.	2
4327	Find $ a_{ 432 } $ of an arithmetic progression if $ a_1 = 105 ~~ \text{and} ~~ d = \left( -9 \right) $.	2
4328	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 2 $.	2
4329	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 1 $.	2
4330	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 10 $.	2
4331	$$ a_1 = -95 ~,~ d = -10 ~,~ a_n = 21 ~,~ n = ? $$	2
4332	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = -23 ~~ \text{and} ~~ d = 4 $.	2
4333	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 4 $.	2
4334	Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = \frac{ 101 }{ 100 } ~~ \text{and} ~~ d = \frac{ 1 }{ 100 } $.	2
4335	Find $ d $ (common difference of arithmetic progression) if $ a_1 = 16 ~~ \text{and} ~~ S_{ 163 } = 4475 $.	2
4336	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 159 ~~ \text{and} ~~ d = \left( -10 \right) $.	2
4337	Find $ a_{ 1001 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
4338	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 138 ~~ \text{and} ~~ d = \left( -10 \right) $.	2
4339	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 138 ~~ \text{and} ~~ d = -10 $.	2
4340	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 69 ~~ \text{and} ~~ d = \left( -10 \right) $.	2
4341	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 7 $.	2
4342	Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 7 $.	2
4343	Find $ a_{ 44 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 8 $.	2
4344	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
4345	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = \left( -12 \right) $.	2
4346	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 38 ~~ \text{and} ~~ d = 0 $.	2
4347	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 38 ~~ \text{and} ~~ d = 0 $.	2
4348	Find $ a_{ 973 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = \left( -10 \right) $.	2
4349	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = -17 ~~ \text{and} ~~ d = 5 $.	2
4350	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 37 ~~ \text{and} ~~ d = -3 $.	2