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
3201	Find $ S_{ 32 } $ ( sum of first $ 32 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
3202	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
3203	Find $ a_{ 51 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = \left( -13 \right) $.	2
3204	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 86 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
3205	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 7 $.	2
3206	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 4 $.	2
3207	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 9 $.	2
3208	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	2
3209	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	2
3210	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	2
3211	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ d = \frac{ 6 }{ 5 } $.	2
3212	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 13 $.	2
3213	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 0 $.	2
3214	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	2
3215	Find $ a_{ 950 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	2
3216	Find $ a_{ 600 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	2
3217	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = -31 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
3218	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = -63 ~~ \text{and} ~~ d = 6 $.	2
3219	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 100 $.	2
3220	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 6 $.	2
3221	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 72 ~~ \text{and} ~~ d = \left( -24 \right) $.	2
3222	Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = 55 ~~ \text{and} ~~ d = 2 $.	2
3223	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 20 $.	2
3224	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 22 ~~ \text{and} ~~ d = 20 $.	2
3225	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 46850 ~~ \text{and} ~~ d = 1400 $.	2
3226	Find $ S_{ 208 } $ ( sum of first $ 208 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
3227	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = -24 ~~ \text{and} ~~ d = 2 $.	2
3228	Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 2 $.	2
3229	Find $ a_{ 39 } $ of an arithmetic progression if $ a_1 = -22 ~~ \text{and} ~~ d = \left( -10 \right) $.	2
3230	Find $ a_{ 26 } $ of an arithmetic progression if $ a_1 = -38 ~~ \text{and} ~~ d = \left( -8 \right) $.	2
3231	Find $ S_{ 38 } $ ( sum of first $ 38 $ terms ) of arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 5 $.	2
3232	Find $ a_{ 38 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 5 $.	2
3233	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
3234	Find common difference $ d $ of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ a_{ 4 } = 15 $.	2
3235	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 2 $.	2
3236	$$ a_1 = 5 ~,~ d = \frac{ 10 }{ 3 } ~,~ a_n = 4 ~,~ n = ? $$	2
3237	Find $ S_{ 296 } $ ( sum of first $ 296 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	2
3238	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ d = 2 $.	2
3239	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
3240	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 3 $.	2
3241	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 34 ~~ \text{and} ~~ d = 3 $.	2
3242	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 5 $.	2
3243	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 0 $.	2
3244	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 6 $.	2
3245	Find $ a_{ 2786 } $ of an arithmetic progression if $ a_1 = \frac{ 273 }{ 10 } ~~ \text{and} ~~ d = \frac{ 457 }{ 25 } $.	2
3246	Find $ S_{ 2786 } $ ( sum of first $ 2786 $ terms ) of arithmetic progression if $ a_1 = \frac{ 273 }{ 10 } ~~ \text{and} ~~ d = \frac{ 457 }{ 25 } $.	2
3247	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -\frac{ 9 }{ 4 } \right) $.	2
3248	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 403 ~~ \text{and} ~~ d = \left( -8 \right) $.	2
3249	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 37 ~~ \text{and} ~~ d = 5 $.	2
3250	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 37 ~~ \text{and} ~~ d = 5 $.	2