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
3951	Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $.	2
3952	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 4 $.	2
3953	Find $ S_{ 140 } $ ( sum of first $ 140 $ terms ) of arithmetic progression if $ a_1 = 2700 ~~ \text{and} ~~ d = 25 $.	2
3954	$$ a_1 = 3 ~,~ d = 4 ~,~ a_n = 38 ~,~ n = ? $$	2
3955	Find $ a_1 $ (first term of arithmetic progression) if $ d = -4 ~~ \text{and} ~~ a_{ 37 } = 10 $.	2
3956	Find $ a_{ 210 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 0 $.	2
3957	$$ a_1 = -23 ~,~ d = -6 ~,~ S_n = -175 ~,~ n = ? $$	2
3958	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 31 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
3959	$$ a_1 = 11 ~,~ d = 6 ~,~ a_n = 365 ~,~ n = ? $$	2
3960	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 31 ~~ \text{and} ~~ d = 4 $.	2
3961	Find $ S_{ 82 } $ ( sum of first $ 82 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
3962	Find $ S_{ 60 } $ ( sum of first $ 60 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 1000 $.	2
3963	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 2000 ~~ \text{and} ~~ d = 2000 $.	2
3964	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 2000 ~~ \text{and} ~~ d = 2000 $.	2
3965	Find $ S_{ 1 } $ ( sum of first $ 1 $ terms ) of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	2
3966	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	2
3967	$$ a_1 = 306 ~,~ d = 6 ~,~ a_n = 486 ~,~ n = ? $$	2
3968	Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	2
3969	Find $ a_1 $ (first term of arithmetic progression) if $ d = 5 ~~ \text{and} ~~ a_{ 20 } = 97 $.	2
3970	Find $ S_{ 246 } $ ( sum of first $ 246 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
3971	Find $ S_{ 201 } $ ( sum of first $ 201 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	2
3972	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 2 $.	2
3973	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 78 ~~ \text{and} ~~ d = 1 $.	2
3974	Find $ S_{ 32 } $ ( sum of first $ 32 $ terms ) of arithmetic progression if $ a_1 = 78 ~~ \text{and} ~~ d = 1 $.	2
3975	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 22 ~~ \text{and} ~~ d = -6 $.	2
3976	Find $ a_{ 42 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	2
3977	Find common difference $ d $ of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ a_{ 205 } = 100 $.	2
3978	$$ a_1 = 95 ~,~ d = -5 ~,~ S_n = 0 ~,~ n = ? $$	2
3979	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = -8 $.	2
3980	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 10 $.	2
3981	Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 7 $.	2
3982	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
3983	Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = 36 ~~ \text{and} ~~ d = \left( -10 \right) $.	2
3984	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 3 $.	2
3985	$$ a_1 = 7 ~,~ d = 3 ~,~ a_n = 130 ~,~ n = ? $$	2
3986	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	2
3987	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 6 $.	2
3988	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
3989	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = -7 $.	2
3990	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 9 $.	2
3991	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = \left( -9 \right) $.	2
3992	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 56 ~~ \text{and} ~~ d = \left( -10 \right) $.	2
3993	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -22 ~~ \text{and} ~~ d = 8 $.	2
3994	Find $ a_{ 250 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 5 $.	2
3995	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 5 $.	2
3996	Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 6 $.	2
3997	Find $ a_{ 36 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 10 $.	2
3998	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 13 $.	2
3999	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 1 $.	2
4000	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 7 $.	2