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
9201	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = \frac{ 10 }{ 11 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 11 } \right) $.	1
9202	Find $ a_{ 67 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 3 $.	1
9203	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 250 ~~ \text{and} ~~ d = 1 $.	1
9204	Find $ a_{ 57 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 8 $.	1
9205	$$ a_1 = -12 ~,~ d = 11 ~,~ a_n = 53 ~,~ n = ? $$	1
9206	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 85 ~~ \text{and} ~~ d = 10 $.	1
9207	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 1 $.	1
9208	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 1 $.	1
9209	Find $ S_{ 28 } $ ( sum of first $ 28 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 1 $.	1
9210	Find $ S_{ 27 } $ ( sum of first $ 27 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 1 $.	1
9211	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
9212	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
9213	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 4 $.	1
9214	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 13 $.	1
9215	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 16 $.	1
9216	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = 22 $.	1
9217	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	1
9218	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -53 ~~ \text{and} ~~ d = \left( -53 \right) $.	1
9219	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 1 $.	1
9220	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 8 $.	1
9221	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 8 $.	1
9222	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 8 $.	1
9223	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 8 $.	1
9224	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 2 $.	1
9225	Find $ S_{ 45 } $ ( sum of first $ 45 $ terms ) of arithmetic progression if $ a_1 = 240 ~~ \text{and} ~~ d = -4 $.	1
9226	Find common difference $ d $ of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ a_{ 2 } = 84 $.	1
9227	Find common difference $ d $ of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ a_{ 2 } = 48 $.	1
9228	Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	1
9229	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	1
9230	Find $ S_{ 2016 } $ ( sum of first $ 2016 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 1 $.	1
9231	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 7 $.	1
9232	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 7 $.	1
9233	Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	1
9234	Find $ S_{ 78 } $ ( sum of first $ 78 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	1
9235	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 8 $.	1
9236	Find $ S_{ 95 } $ ( sum of first $ 95 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	1
9237	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 51 ~~ \text{and} ~~ d = 3 $.	1
9238	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 86 ~~ \text{and} ~~ d = 7 $.	1
9239	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = \frac{ 23 }{ 10 } ~~ \text{and} ~~ d = \frac{ 4 }{ 5 } $.	1
9240	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = \frac{ 117 }{ 10 } ~~ \text{and} ~~ d = \frac{ 9 }{ 10 } $.	1
9241	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 250 ~~ \text{and} ~~ d = 100 $.	1
9242	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 250 ~~ \text{and} ~~ d = 100 $.	1
9243	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 250 ~~ \text{and} ~~ d = 100 $.	1
9244	Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = 259 ~~ \text{and} ~~ d = 100 $.	1
9245	Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = 250 ~~ \text{and} ~~ d = 100 $.	1
9246	Find $ S_{ 2 } $ ( sum of first $ 2 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $.	1
9247	$$ a_1 = 7 ~,~ a_n = 20 ~,~ S_n = 1090 ~,~ n = ? $$	1
9248	$$ d = 6 ~,~ a_n = 80 ~,~ S_n = 50 ~,~ n = ? $$	1
9249	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = \frac{ 71 }{ 4 } ~~ \text{and} ~~ d = \frac{ 17 }{ 4 } $.	1
9250	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = \frac{ 71 }{ 4 } ~~ \text{and} ~~ d = \frac{ 17 }{ 4 } $.	1