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
3151	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 5 $.	2
3152	Find $ S_{ 2 } $ ( sum of first $ 2 $ terms ) of arithmetic progression if $ a_1 = 29 ~~ \text{and} ~~ d = 2 $.	2
3153	Find $ a_{ 42 } $ of an arithmetic progression if $ a_1 = 313 ~~ \text{and} ~~ d = \left( -6 \right) $.	2
3154	Find $ a_{ 49 } $ of an arithmetic progression if $ a_1 = 253 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
3155	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = \frac{ 5 }{ 3 } ~~ \text{and} ~~ d = \frac{ 4 }{ 3 } $.	2
3156	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $.	2
3157	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \frac{ 7 }{ 10 } $.	2
3158	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	2
3159	Find $ a_1 $ (first term of arithmetic progression) if $ d = -7 ~~ \text{and} ~~ a_{ 13 } = 15 $.	2
3160	Find $ S_{ 53 } $ ( sum of first $ 53 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	2
3161	Find $ a_{ 39 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 3 $.	2
3162	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = \left( -8 \right) $.	2
3163	Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $.	2
3164	Find $ a_{ 37 } $ of an arithmetic progression if $ a_1 = -19 ~~ \text{and} ~~ d = \left( -8 \right) $.	2
3165	Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = -36 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
3166	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = -32 ~~ \text{and} ~~ d = 5 $.	2
3167	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $.	2
3168	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $.	2
3169	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $.	2
3170	Find $ a_{ 51 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
3171	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 5 $.	2
3172	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
3173	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 5 $.	2
3174	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	2
3175	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -1 \right) $.	2
3176	$$ a_1 = 48 ~,~ a_n = 33 ~,~ S_n = 1536 ~,~ n = ? $$	2
3177	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 48 ~~ \text{and} ~~ d = 0 $.	2
3178	Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 0 $.	2
3179	Find $ a_1 $ (first term of arithmetic progression) if $ d = 2 ~~ \text{and} ~~ S_{ 33 } = 1536 $.	2
3180	Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = 48 ~~ \text{and} ~~ d = 2 $.	2
3181	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = \left( -21 \right) $.	2
3182	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
3183	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 5 $.	2
3184	Find $ a_{ 43 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 5 $.	2
3185	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = -4 $.	2
3186	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 52 ~~ \text{and} ~~ d = -4 $.	2
3187	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = -2 $.	2
3188	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = -3 $.	2
3189	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 39 ~~ \text{and} ~~ d = -3 $.	2
3190	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 39 ~~ \text{and} ~~ d = -3 $.	2
3191	Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 39 ~~ \text{and} ~~ d = -3 $.	2
3192	$$ a_1 = 2 ~,~ d = 2 ~,~ a_n = 52 ~,~ n = ? $$	2
3193	Find $ S_{ 52 } $ ( sum of first $ 52 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
3194	$$ a_1 = 4 ~,~ d = 2 ~,~ a_n = 46 ~,~ n = ? $$	2
3195	Find $ S_{ 22 } $ ( sum of first $ 22 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 2 $.	2
3196	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	2
3197	$$ a_{ 2 } = 50 ~~,~~ S_{ 2 } = 18 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
3198	$$ a_{ 2 } = 20 ~~,~~ S_{ 2 } = 20 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
3199	$$ a_1 = 2 ~,~ d = 3 ~,~ a_n = 50 ~,~ n = ? $$	2
3200	$$ a_1 = 3 ~,~ d = 2 ~,~ a_n = 20 ~,~ n = ? $$	2