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
6351	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 3750 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
6352	Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = 41 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
6353	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 13 $.	1
6354	Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	1
6355	Find $ S_{ 998 } $ ( sum of first $ 998 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	1
6356	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 8 $.	1
6357	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 2 $.	1
6358	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 59 ~~ \text{and} ~~ d = -11 $.	1
6359	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 59 ~~ \text{and} ~~ d = \left( -11 \right) $.	1
6360	Find $ S_{ 1 } $ ( sum of first $ 1 $ terms ) of arithmetic progression if $ a_1 = 1200 ~~ \text{and} ~~ d = 1200 $.	1
6361	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 1200 ~~ \text{and} ~~ d = 1200 $.	1
6362	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 1200 ~~ \text{and} ~~ d = 1200 $.	1
6363	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	1
6364	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 12 $.	1
6365	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 12 $.	1
6366	Find $ a_{ 102 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	1
6367	Find $ S_{ 102 } $ ( sum of first $ 102 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	1
6368	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 3 $.	1
6369	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = \left( -6 \right) $.	1
6370	Find $ a_{ 45 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	1
6371	Find $ a_{ 4621 } $ of an arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
6372	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 9 $.	1
6373	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 12 $.	1
6374	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 13 $.	1
6375	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 9 }{ 2 } ~~ \text{and} ~~ d = \frac{ 117 }{ 38 } $.	1
6376	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
6377	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 3 $.	1
6378	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 7 $.	1
6379	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	1
6380	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 0 $.	1
6381	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = 0 $.	1
6382	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = 0 $.	1
6383	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = 2 $.	1
6384	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = 3 $.	1
6385	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = \frac{ 7 }{ 2 } $.	1
6386	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = 4 $.	1
6387	Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ d = \frac{ 1 }{ 100 } $.	1
6388	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = 4 $.	1
6389	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 5 $.	1
6390	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 3 }{ 4 } $.	1
6391	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = -2 $.	1
6392	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
6393	Find $ S_{ 1760 } $ ( sum of first $ 1760 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 10 $.	1
6394	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = -10 $.	1
6395	Find $ S_{ 66 } $ ( sum of first $ 66 $ terms ) of arithmetic progression if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $.	1
6396	Find $ S_{ 52 } $ ( sum of first $ 52 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 0 $.	1
6397	Find $ S_{ 52 } $ ( sum of first $ 52 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 1 $.	1
6398	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 20 $.	1
6399	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = \frac{ 11 }{ 2 } ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $.	1
6400	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 6 $.	1