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
3851	Find $ S_{ 202 } $ ( sum of first $ 202 $ terms ) of arithmetic progression if $ a_1 = -100 ~~ \text{and} ~~ d = 102 $.	2
3852	Find $ a_{ 94 } $ of an arithmetic progression if $ a_1 = -26 ~~ \text{and} ~~ d = \left( -9 \right) $.	2
3853	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = -22 ~~ \text{and} ~~ d = \frac{ 2 }{ 3 } $.	2
3854	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 0 $.	2
3855	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = 6 $.	2
3856	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 12 $.	2
3857	Find $ a_{ 65 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \left( -15 \right) $.	2
3858	Find $ a_{ 49 } $ of an arithmetic progression if $ a_1 = 49 ~~ \text{and} ~~ d = 3 $.	2
3859	Find $ a_{ 837 } $ of an arithmetic progression if $ a_1 = -80 ~~ \text{and} ~~ d = 5 $.	2
3860	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = -80 ~~ \text{and} ~~ d = 5 $.	2
3861	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = -80 ~~ \text{and} ~~ d = 5 $.	2
3862	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 20 $.	2
3863	Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 6 $.	2
3864	Find $ S_{ 29 } $ ( sum of first $ 29 $ terms ) of arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 10 $.	2
3865	Find $ S_{ 29 } $ ( sum of first $ 29 $ terms ) of arithmetic progression if $ a_1 = 250 ~~ \text{and} ~~ d = 100 $.	2
3866	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 153 ~~ \text{and} ~~ d = 3 $.	2
3867	Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	2
3868	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = -6 $.	2
3869	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	2
3870	Find $ S_{ 77 } $ ( sum of first $ 77 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
3871	$$ a_1 = 179 ~,~ d = 39 ~,~ S_n = 69219 ~,~ n = ? $$	2
3872	$$ a_1 = 179 ~,~ d = 39 ~,~ S_n = 34219 ~,~ n = ? $$	2
3873	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	2
3874	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 2 }{ 5 } $.	2
3875	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 48 ~~ \text{and} ~~ d = -3 $.	2
3876	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = -18 ~~ \text{and} ~~ d = 3 $.	2
3877	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 4 $.	2
3878	$$ a_1 = 6 ~,~ d = 4 ~,~ a_n = 90 ~,~ n = ? $$	2
3879	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 4 $.	2
3880	Find $ S_{ 22 } $ ( sum of first $ 22 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 4 $.	2
3881	$$ a_1 = -10 ~,~ d = 3 ~,~ S_n = 200 ~,~ n = ? $$	2
3882	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = -14 ~~ \text{and} ~~ d = 2 $.	2
3883	Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = -3 $.	2
3884	$$ a_1 = 1 ~,~ d = \frac{ 1 }{ 3 } ~,~ a_n = 100 ~,~ n = ? $$	2
3885	Find $ S_{ 298 } $ ( sum of first $ 298 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	2
3886	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = 3 $.	2
3887	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 0 $.	2
3888	Find $ S_{ 2023 } $ ( sum of first $ 2023 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $.	2
3889	Find $ S_{ 77 } $ ( sum of first $ 77 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	2
3890	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = \frac{ 7 }{ 3 } ~~ \text{and} ~~ d = \left( -\frac{ 10 }{ 3 } \right) $.	2
3891	Find $ S_{ 730 } $ ( sum of first $ 730 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
3892	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 100 $.	2
3893	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = -13 ~~ \text{and} ~~ d = 8 $.	2
3894	Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 4 $.	2
3895	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = 8 $.	2
3896	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
3897	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = 4 $.	2
3898	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
3899	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
3900	$$ a_1 = 10 ~~,~~ d = -10 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2