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
8351	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 13 }{ 8 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	1
8352	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 7 $.	1
8353	Find $ a_{ 76 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 8 $.	1
8354	Find $ a_{ 57 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 4 $.	1
8355	Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 6 $.	1
8356	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = -3 $.	1
8357	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \frac{ 11 }{ 5 } $.	1
8358	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 6 $.	1
8359	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = \left( -4 \right) $.	1
8360	Find $ a_{ 65 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
8361	Find $ a_{ 66 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
8362	Find $ a_{ 93 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $.	1
8363	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 5 $.	1
8364	Find $ a_{ 56 } $ of an arithmetic progression if $ a_1 = 22 ~~ \text{and} ~~ d = 5 $.	1
8365	$$ a_1 = 4 ~,~ d = 4 ~,~ S_n = 4 ~,~ n = ? $$	1
8366	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 7 $.	1
8367	Find $ S_{ 415 } $ ( sum of first $ 415 $ terms ) of arithmetic progression if $ a_1 = 5800000 ~~ \text{and} ~~ d = 10000 $.	1
8368	Find $ S_{ 67 } $ ( sum of first $ 67 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	1
8369	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 9 $.	1
8370	Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = \frac{ 23 }{ 10 } ~~ \text{and} ~~ d = \left( -\frac{ 23 }{ 10 } \right) $.	1
8371	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = \frac{ 99 }{ 20 } ~~ \text{and} ~~ d = \frac{ 379 }{ 20 } $.	1
8372	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 219 ~~ \text{and} ~~ d = 10 $.	1
8373	Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \left( -4 \right) $.	1
8374	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	1
8375	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 4 $.	1
8376	Find $ S_{ 35 } $ ( sum of first $ 35 $ terms ) of arithmetic progression if $ a_1 = 150 ~~ \text{and} ~~ d = 50 $.	1
8377	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 900 ~~ \text{and} ~~ d = 900 $.	1
8378	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 900 ~~ \text{and} ~~ d = 900 $.	1
8379	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 900 ~~ \text{and} ~~ d = 900 $.	1
8380	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 900 ~~ \text{and} ~~ d = 900 $.	1
8381	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -14 ~~ \text{and} ~~ d = 4 $.	1
8382	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = -14 ~~ \text{and} ~~ d = 4 $.	1
8383	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ d = \frac{ 3 }{ 4 } $.	1
8384	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ d = \frac{ 3 }{ 4 } $.	1
8385	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 0 $.	1
8386	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
8387	Find $ S_{ 3 } $ ( sum of first $ 3 $ terms ) of arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = -5 $.	1
8388	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 11 }{ 8 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	1
8389	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 11 }{ 8 } ~~ \text{and} ~~ d = 23 $.	1
8390	Find $ S_{ 117 } $ ( sum of first $ 117 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	1
8391	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 18 $.	1
8392	Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $.	1
8393	Find $ S_{ 23 } $ ( sum of first $ 23 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 200 $.	1
8394	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 1400 ~~ \text{and} ~~ d = 200 $.	1
8395	Find $ S_{ 38 } $ ( sum of first $ 38 $ terms ) of arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = -37 $.	1
8396	Find $ S_{ 23 } $ ( sum of first $ 23 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 0 $.	1
8397	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 8 $.	1
8398	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 300 ~~ \text{and} ~~ d = -3 $.	1
8399	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 34 ~~ \text{and} ~~ d = 4 $.	1
8400	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ d = \frac{ 1 }{ 100 } $.	1