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
3701	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
3702	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
3703	Find $ S_{ 56 } $ ( sum of first $ 56 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	2
3704	Find $ a_1 $ (first term of arithmetic progression) if $ d = 4 ~~ \text{and} ~~ S_{ 56 } = 19488 $.	2
3705	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 37 ~~ \text{and} ~~ d = 5 $.	2
3706	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
3707	Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
3708	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
3709	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 0 $.	2
3710	Find $ a_{ 41 } $ of an arithmetic progression if $ a_1 = 230 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
3711	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 3 $.	2
3712	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 44 ~~ \text{and} ~~ d = 3 $.	2
3713	Find $ S_{ 73 } $ ( sum of first $ 73 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	2
3714	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 6 $.	2
3715	Find $ S_{ 43 } $ ( sum of first $ 43 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 5 $.	2
3716	Find $ S_{ 44 } $ ( sum of first $ 44 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 5 $.	2
3717	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $.	2
3718	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 6 $.	2
3719	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 24 $.	2
3720	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -74 ~~ \text{and} ~~ d = -3 $.	2
3721	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 99 ~~ \text{and} ~~ d = 14 $.	2
3722	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 200 $.	2
3723	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	2
3724	$$ a_{ 5 } = 30 ~~,~~ S_{ 5 } = 28 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
3725	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 3 $.	2
3726	$$ a_1 = 2 ~,~ d = 3 ~,~ S_n = 30 ~,~ n = ? $$	2
3727	Find $ S_{ 35 } $ ( sum of first $ 35 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 3 $.	2
3728	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 2 $.	2
3729	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 17 $.	2
3730	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 3 $.	2
3731	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 7 $.	2
3732	$$ a_1 = 14 ~,~ d = 13 ~,~ a_n = 235 ~,~ n = ? $$	2
3733	Find $ a_{ 90 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
3734	Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
3735	Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
3736	Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
3737	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
3738	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = \frac{ 8 }{ 3 } ~~ \text{and} ~~ d = -\frac{ 1 }{ 3 } $.	2
3739	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = \left( -6 \right) $.	2
3740	Find $ a_{ 36 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 3 $.	2
3741	Find $ S_{ 120 } $ ( sum of first $ 120 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 7 $.	2
3742	$$ a_1 = -6 ~,~ d = 3 ~,~ a_n = 12 ~,~ n = ? $$	2
3743	Find $ a_1 $ (first term of arithmetic progression) if $ d = -6 ~~ \text{and} ~~ a_{ 91 } = -521 $.	2
3744	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	2
3745	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 7 $.	2
3746	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = \frac{ 7 }{ 2 } ~~ \text{and} ~~ d = \left( -\frac{ 3 }{ 2 } \right) $.	2
3747	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = -2 $.	2
3748	Find $ S_{ 60 } $ ( sum of first $ 60 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = -9 $.	2
3749	Find $ S_{ 220 } $ ( sum of first $ 220 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 25 $.	2
3750	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 72 ~~ \text{and} ~~ d = \frac{ 2 }{ 3 } $.	2