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
4251	Find $ S_{ 3 } $ ( sum of first $ 3 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 8 $.	2
4252	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ d = 1 $.	2
4253	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = \frac{ 51 }{ 10 } ~~ \text{and} ~~ d = \left( -\frac{ 21 }{ 5 } \right) $.	2
4254	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
4255	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
4256	Find $ a_{ 45 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
4257	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = \left( -77 \right) $.	2
4258	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
4259	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 5 $.	2
4260	$$ a_1 = 50 ~~,~~ d = 7 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
4261	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 7 $.	2
4262	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = \frac{ 23 }{ 7 } ~~ \text{and} ~~ d = \frac{ 6 }{ 7 } $.	2
4263	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $.	2
4264	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $.	2
4265	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = \frac{ 31 }{ 2 } ~~ \text{and} ~~ d = -\frac{ 1 }{ 2 } $.	2
4266	Find $ a_{ 90 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $.	2
4267	Find $ S_{ 90 } $ ( sum of first $ 90 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $.	2
4268	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = 3 $.	2
4269	Find $ a_{ 57 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
4270	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 22 $.	2
4271	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \frac{ 12 }{ 5 } $.	2
4272	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 5000 ~~ \text{and} ~~ d = 5000 $.	2
4273	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 5000 ~~ \text{and} ~~ d = 5000 $.	2
4274	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	2
4275	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 1 $.	2
4276	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 1024 $.	2
4277	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 256 $.	2
4278	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 150 $.	2
4279	Find common difference $ d $ of arithmetic progression if $ a_1 = 42 ~~ \text{and} ~~ a_{ 4 } = 146 $.	2
4280	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -18 ~~ \text{and} ~~ d = 8 $.	2
4281	Find $ a_{ 44 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
4282	Find $ S_{ 44 } $ ( sum of first $ 44 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = -2 $.	2
4283	Find $ d $ (common difference of arithmetic progression) if $ a_1 = 8 ~~ \text{and} ~~ S_{ 50 } = 4750 $.	2
4284	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = -20 $.	2
4285	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
4286	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = -3 $.	2
4287	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 4 $.	2
4288	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 7 $.	2
4289	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 6 $.	2
4290	Find $ a_{ 1000 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 1 }{ 100 } $.	2
4291	Find $ a_{ 69 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 6 $.	2
4292	Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 14 $.	2
4293	Find common difference $ d $ of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ a_{ 3 } = 57 $.	2
4294	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = \left( -\frac{ 3 }{ 5 } \right) $.	2
4295	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
4296	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
4297	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 7 $.	2
4298	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 0 $.	2
4299	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 53 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
4300	Find $ a_{ 148 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $.	2