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
3051	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	2
3052	Find $ a_1 $ (first term of arithmetic progression) if $ d = -4 ~~ \text{and} ~~ a_{ 11 } = 15 $.	2
3053	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
3054	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -35 ~~ \text{and} ~~ d = 0 $.	2
3055	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -35 ~~ \text{and} ~~ d = 5 $.	2
3056	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 47 ~~ \text{and} ~~ d = 5 $.	2
3057	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 47 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
3058	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = -30 $.	2
3059	$$ a_1 = 15 ~,~ d = -6 ~,~ a_n = 15 ~,~ n = ? $$	2
3060	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = 7 $.	2
3061	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 0 $.	2
3062	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 4 } \right) $.	2
3063	Find $ a_{ 96 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = \left( -12 \right) $.	2
3064	Find $ a_{ 54 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = 5 $.	2
3065	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = -\frac{ 5 }{ 2 } ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $.	2
3066	Find $ a_{ 91 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 5 $.	2
3067	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ d = \left( -50 \right) $.	2
3068	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 4 $.	2
3069	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 4 $.	2
3070	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = -5 $.	2
3071	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 5 $.	2
3072	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
3073	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $.	2
3074	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ d = -\frac{ 1 }{ 2 } $.	2
3075	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	2
3076	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	2
3077	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 9 $.	2
3078	Find $ S_{ 1400 } $ ( sum of first $ 1400 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 8 $.	2
3079	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	2
3080	$$ a_1 = 1 ~,~ d = 2 ~,~ a_n = 499 ~,~ n = ? $$	2
3081	$$ a_1 = 1 ~,~ d = 2 ~,~ a_n = 301 ~,~ n = ? $$	2
3082	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	2
3083	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 9 $.	2
3084	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 270 ~~ \text{and} ~~ d = 25 $.	2
3085	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 270 ~~ \text{and} ~~ d = 25 $.	2
3086	Find common difference $ d $ of arithmetic progression if $ a_1 = 1285 ~~ \text{and} ~~ a_{ 6 } = 1700 $.	2
3087	Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = -\frac{ 6 }{ 25 } $.	2
3088	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 3 $.	2
3089	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 63 ~~ \text{and} ~~ d = 6 $.	2
3090	Find $ S_{ 47 } $ ( sum of first $ 47 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 5 $.	2
3091	Find $ a_{ 48 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 5 $.	2
3092	Find $ S_{ 48 } $ ( sum of first $ 48 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 7 $.	2
3093	Find $ S_{ 36 } $ ( sum of first $ 36 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 6 $.	2
3094	Find $ S_{ 46 } $ ( sum of first $ 46 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 3 $.	2
3095	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = -4 $.	2
3096	Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = 33 ~~ \text{and} ~~ d = -\frac{ 8 }{ 5 } $.	2
3097	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = -2 $.	2
3098	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = -4 $.	2
3099	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 306 ~~ \text{and} ~~ d = -1 $.	2
3100	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 103 ~~ \text{and} ~~ d = -\frac{ 64 }{ 5 } $.	2