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
3751	$$ a_1 = 7 ~,~ d = -11 ~,~ a_n = 34 ~,~ n = ? $$	2
3752	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
3753	$$ a_1 = 200 ~,~ d = -5 ~,~ a_n = 41 ~,~ n = ? $$	2
3754	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 250 ~~ \text{and} ~~ d = 75 $.	2
3755	$$ a_1 = 250 ~,~ d = 75 ~,~ a_n = 775 ~,~ n = ? $$	2
3756	$$ a_1 = 250 ~,~ d = 75 ~,~ S_n = 2000 ~,~ n = ? $$	2
3757	$$ a_1 = -4 ~~,~~ d = 9 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
3758	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 6 $.	2
3759	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 2 $.	2
3760	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
3761	$$ a_1 = 2 ~,~ d = 2 ~,~ S_n = 100 ~,~ n = ? $$	2
3762	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 6 $.	2
3763	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 6 $.	2
3764	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 6 $.	2
3765	Find $ S_{ 51 } $ ( sum of first $ 51 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 13 $.	2
3766	Find $ S_{ 82 } $ ( sum of first $ 82 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = -3 $.	2
3767	Find $ S_{ 200 } $ ( sum of first $ 200 $ terms ) of arithmetic progression if $ a_1 = 2505 ~~ \text{and} ~~ d = 5 $.	2
3768	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 860 ~~ \text{and} ~~ d = 1 $.	2
3769	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 860 ~~ \text{and} ~~ d = 1 $.	2
3770	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 859 ~~ \text{and} ~~ d = 1 $.	2
3771	Find $ S_{ 105 } $ ( sum of first $ 105 $ terms ) of arithmetic progression if $ a_1 = 854 ~~ \text{and} ~~ d = 1 $.	2
3772	$$ a_1 = 2 ~,~ d = 8 ~,~ a_n = 15 ~,~ n = ? $$	2
3773	Find $ S_{ 109 } $ ( sum of first $ 109 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $.	2
3774	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	2
3775	Find $ S_{ 42 } $ ( sum of first $ 42 $ terms ) of arithmetic progression if $ a_1 = 42 ~~ \text{and} ~~ d = 0 $.	2
3776	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 42 ~~ \text{and} ~~ d = 0 $.	2
3777	Find $ a_{ 98 } $ of an arithmetic progression if $ a_1 = 840 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
3778	Find $ a_{ 90 } $ of an arithmetic progression if $ a_1 = -40 ~~ \text{and} ~~ d = 2 $.	2
3779	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = -9 $.	2
3780	Find $ S_{ 71 } $ ( sum of first $ 71 $ terms ) of arithmetic progression if $ a_1 = 1001 ~~ \text{and} ~~ d = 3 $.	2
3781	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $.	2
3782	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = 1 $.	2
3783	Find $ a_{ 135 } $ of an arithmetic progression if $ a_1 = 106 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
3784	Find $ a_{ 39 } $ of an arithmetic progression if $ a_1 = -37 ~~ \text{and} ~~ d = 4 $.	2
3785	Find $ S_{ 1 } $ ( sum of first $ 1 $ terms ) of arithmetic progression if $ a_1 = 150 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
3786	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 150 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
3787	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 150 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
3788	Find $ S_{ 315 } $ ( sum of first $ 315 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	2
3789	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $.	2
3790	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 5 $.	2
3791	Find $ S_{ 75 } $ ( sum of first $ 75 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 0 $.	2
3792	Find $ S_{ 75 } $ ( sum of first $ 75 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
3793	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	2
3794	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 5 $.	2
3795	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = -\frac{ 5 }{ 3 } ~~ \text{and} ~~ d = \frac{ 2 }{ 3 } $.	2
3796	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 106 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
3797	Find $ a_1 $ (first term of arithmetic progression) if $ d = 3 ~~ \text{and} ~~ a_{ 16 } = 48 $.	2
3798	Find $ a_1 $ (first term of arithmetic progression) if $ d = -3 ~~ \text{and} ~~ a_{ 14 } = -28 $.	2
3799	Find $ S_{ 60 } $ ( sum of first $ 60 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 3 $.	2
3800	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = -2 $.	2