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
3101	Find $ S_{ 133 } $ ( sum of first $ 133 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = -\frac{ 3 }{ 100 } $.	2
3102	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = -\frac{ 4 }{ 5 } $.	2
3103	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = -1 $.	2
3104	Find $ S_{ 22 } $ ( sum of first $ 22 $ terms ) of arithmetic progression if $ a_1 = 70 ~~ \text{and} ~~ d = -\frac{ 16 }{ 5 } $.	2
3105	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 29 ~~ \text{and} ~~ d = -4 $.	2
3106	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 37 ~~ \text{and} ~~ d = -\frac{ 32 }{ 5 } $.	2
3107	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 31 ~~ \text{and} ~~ d = 12 $.	2
3108	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 120 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
3109	$$ a_1 = 1 ~,~ d = 1 ~,~ S_n = 1416 ~,~ n = ? $$	2
3110	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	2
3111	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = \frac{ 3 }{ 4 } ~~ \text{and} ~~ d = \frac{ 2 }{ 5 } $.	2
3112	Find $ a_{ 66 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 3 $.	2
3113	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
3114	Find $ S_{ 1 } $ ( sum of first $ 1 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = -1 $.	2
3115	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 198 ~~ \text{and} ~~ d = 2 $.	2
3116	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 50 $.	2
3117	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	2
3118	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 13 $.	2
3119	Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 1 $.	2
3120	Find $ S_{ 101 } $ ( sum of first $ 101 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	2
3121	Find $ a_{ 63 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 7 $.	2
3122	Find $ a_{ 72 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 3 $.	2
3123	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = \left( -9 \right) $.	2
3124	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 4 $.	2
3125	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 0 $.	2
3126	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = \frac{ 73 }{ 5 } $.	2
3127	Find $ a_{ 59 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 5 $.	2
3128	Find $ S_{ 692 } $ ( sum of first $ 692 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 1 $.	2
3129	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $.	2
3130	$$ a_1 = -4 ~,~ d = -1 ~,~ a_n = 0 ~,~ n = ? $$	2
3131	$$ a_1 = -4 ~,~ d = 3 ~,~ a_n = 0 ~,~ n = ? $$	2
3132	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 5 $.	2
3133	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 52 ~~ \text{and} ~~ d = \left( -6 \right) $.	2
3134	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 6 $.	2
3135	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \frac{ 9 }{ 2 } $.	2
3136	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = \frac{ 13 }{ 2 } ~~ \text{and} ~~ d = -2 $.	2
3137	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	2
3138	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 31 ~~ \text{and} ~~ d = 2 $.	2
3139	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 1 $.	2
3140	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 1 $.	2
3141	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 1 $.	2
3142	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 11 $.	2
3143	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = \left( -11 \right) $.	2
3144	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 9 $.	2
3145	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = \left( -\frac{ 4 }{ 5 } \right) $.	2
3146	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
3147	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = -2 $.	2
3148	Find $ a_{ 42 } $ of an arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = 3 $.	2
3149	$$ a_1 = 492 ~,~ a_n = 4 ~,~ S_n = 300 ~,~ n = ? $$	2
3150	Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 18 $.	2