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
8501	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 7 $.	1
8502	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = \left( -8 \right) $.	1
8503	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = -4 $.	1
8504	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = -4 $.	1
8505	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = -4 $.	1
8506	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = \left( -4 \right) $.	1
8507	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = -3 $.	1
8508	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
8509	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = -3 $.	1
8510	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
8511	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = -3 $.	1
8512	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = -3 $.	1
8513	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -14 ~~ \text{and} ~~ d = 6 $.	1
8514	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = -14 ~~ \text{and} ~~ d = 6 $.	1
8515	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 1 }{ 4 } ~~ \text{and} ~~ d = \frac{ 5 }{ 3 } $.	1
8516	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 1 }{ 4 } ~~ \text{and} ~~ d = \frac{ 5 }{ 3 } $.	1
8517	Find $ S_{ 154 } $ ( sum of first $ 154 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ d = \frac{ 1 }{ 100 } $.	1
8518	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 1 }{ 4 } ~~ \text{and} ~~ d = \frac{ 5 }{ 3 } $.	1
8519	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 5 } \right) $.	1
8520	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = -\frac{ 1 }{ 5 } $.	1
8521	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = \frac{ 2 }{ 3 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	1
8522	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = \frac{ 2 }{ 3 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	1
8523	Find $ a_{ 59 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	1
8524	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = -35 ~~ \text{and} ~~ d = \left( -10 \right) $.	1
8525	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = \left( -8 \right) $.	1
8526	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = \frac{ 5 }{ 4 } ~~ \text{and} ~~ d = \frac{ 23 }{ 8 } $.	1
8527	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 9 $.	1
8528	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 9 $.	1
8529	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = \frac{ 26 }{ 5 } ~~ \text{and} ~~ d = \frac{ 8 }{ 5 } $.	1
8530	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 7 $.	1
8531	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 4 $.	1
8532	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = -24 ~~ \text{and} ~~ d = 13 $.	1
8533	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 37 ~~ \text{and} ~~ d = 30 $.	1
8534	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = -18 ~~ \text{and} ~~ d = 9 $.	1
8535	Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = -28 ~~ \text{and} ~~ d = \left( -6 \right) $.	1
8536	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = -20 ~~ \text{and} ~~ d = 100 $.	1
8537	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = -38 ~~ \text{and} ~~ d = 100 $.	1
8538	Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = -26 ~~ \text{and} ~~ d = \left( -100 \right) $.	1
8539	Find $ a_{ 37 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 3 $.	1
8540	Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
8541	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = -2 $.	1
8542	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = -26 ~~ \text{and} ~~ d = \frac{ 2 }{ 3 } $.	1
8543	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 26 ~~ \text{and} ~~ d = -3 $.	1
8544	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	1
8545	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = -13 ~~ \text{and} ~~ d = \frac{ 11 }{ 3 } $.	1
8546	$$ a_1 = 2 ~,~ d = 3 ~,~ S_n = 15 ~,~ n = ? $$	1
8547	$$ a_{ 28 } = 166 ~~,~~ S_{ 10 } = 320 ~~,~~ a_1 = ? ~~,~~ d = ? $$	1
8548	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 5 $.	1
8549	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
8550	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = -52 ~~ \text{and} ~~ d = \left( -4 \right) $.	1