Arithmetic sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Arithmetic sequences.

Select category

ID	Problem	Count
3501	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = 8 $.	2
3502	Find $ a_{ 67 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 9 $.	2
3503	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = \left( -8 \right) $.	2
3504	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
3505	Find $ a_{ 69 } $ of an arithmetic progression if $ a_1 = 76 ~~ \text{and} ~~ d = 2 $.	2
3506	$$ a_1 = -14 ~~,~~ d = 4 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
3507	$$ a_1 = -14 ~~,~~ d = 4 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
3508	$$ a_1 = -14 ~,~ d = 4 ~,~ a_n = 5 ~,~ n = ? $$	2
3509	Find $ d $ (common difference of arithmetic progression) if $ a_1 = 22 ~~ \text{and} ~~ S_{ 22 } = 1353 $.	2
3510	Find $ d $ (common difference of arithmetic progression) if $ a_1 = 9 ~~ \text{and} ~~ S_{ 22 } = 1353 $.	2
3511	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 40000 ~~ \text{and} ~~ d = 1600 $.	2
3512	Find common difference $ d $ of arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ a_{ 10 } = -44 $.	2
3513	Find $ a_{ 73 } $ of an arithmetic progression if $ a_1 = 90 ~~ \text{and} ~~ d = \left( -\frac{ 5 }{ 2 } \right) $.	2
3514	Find $ a_{ 76 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	2
3515	Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	2
3516	$$ a_1 = 1000 ~,~ d = 1000 ~,~ S_n = 10000000 ~,~ n = ? $$	2
3517	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	2
3518	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 9 $.	2
3519	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 9 $.	2
3520	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 9 $.	2
3521	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 2 $.	2
3522	Find $ S_{ 28 } $ ( sum of first $ 28 $ terms ) of arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 1 $.	2
3523	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = -3 $.	2
3524	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 4 $.	2
3525	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 3 } \right) $.	2
3526	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ d = \frac{ 1 }{ 8 } $.	2
3527	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 5 $.	2
3528	Find $ a_{ 200 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 5 $.	2
3529	Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 17 $.	2
3530	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 144 ~~ \text{and} ~~ d = \frac{ 28 }{ 5 } $.	2
3531	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 144 ~~ \text{and} ~~ d = \frac{ 28 }{ 5 } $.	2
3532	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 134 ~~ \text{and} ~~ d = \frac{ 28 }{ 5 } $.	2
3533	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 124 ~~ \text{and} ~~ d = \frac{ 28 }{ 5 } $.	2
3534	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 124 ~~ \text{and} ~~ d = \frac{ 28 }{ 5 } $.	2
3535	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 120 ~~ \text{and} ~~ d = \frac{ 28 }{ 5 } $.	2
3536	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 119 ~~ \text{and} ~~ d = \frac{ 28 }{ 5 } $.	2
3537	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 118 ~~ \text{and} ~~ d = \frac{ 28 }{ 5 } $.	2
3538	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 118 ~~ \text{and} ~~ d = \frac{ 28 }{ 5 } $.	2
3539	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 118 ~~ \text{and} ~~ d = 7 $.	2
3540	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 117 ~~ \text{and} ~~ d = 7 $.	2
3541	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 117 ~~ \text{and} ~~ d = 7 $.	2
3542	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 116 ~~ \text{and} ~~ d = 7 $.	2
3543	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 112 ~~ \text{and} ~~ d = \frac{ 28 }{ 5 } $.	2
3544	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 112 ~~ \text{and} ~~ d = \frac{ 28 }{ 5 } $.	2
3545	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 112 ~~ \text{and} ~~ d = \frac{ 28 }{ 5 } $.	2
3546	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 124 ~~ \text{and} ~~ d = \frac{ 28 }{ 5 } $.	2
3547	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 114 ~~ \text{and} ~~ d = \frac{ 28 }{ 5 } $.	2
3548	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 119 ~~ \text{and} ~~ d = \frac{ 56 }{ 9 } $.	2
3549	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 117 ~~ \text{and} ~~ d = \frac{ 56 }{ 9 } $.	2
3550	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 116 ~~ \text{and} ~~ d = \frac{ 56 }{ 9 } $.	2