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
8301	$$ a_1 = 3 ~,~ d = 4 ~,~ S_n = 479 ~,~ n = ? $$	1
8302	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	1
8303	Find $ S_{ 58 } $ ( sum of first $ 58 $ terms ) of arithmetic progression if $ a_1 = 670 ~~ \text{and} ~~ d = 4 $.	1
8304	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 147 ~~ \text{and} ~~ d = -10 $.	1
8305	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	1
8306	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 24 $.	1
8307	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 3 $.	1
8308	Find common difference $ d $ of arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ a_{ 23 } = 79 $.	1
8309	Find $ a_{ 390 } $ of an arithmetic progression if $ a_1 = -378 ~~ \text{and} ~~ d = \frac{ 55 }{ 41 } $.	1
8310	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 29 ~~ \text{and} ~~ d = 0 $.	1
8311	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 450 ~~ \text{and} ~~ d = \frac{ 21 }{ 20 } $.	1
8312	Find $ S_{ 60 } $ ( sum of first $ 60 $ terms ) of arithmetic progression if $ a_1 = 450 ~~ \text{and} ~~ d = \frac{ 21 }{ 20 } $.	1
8313	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 310 ~~ \text{and} ~~ d = 10 $.	1
8314	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 92 ~~ \text{and} ~~ d = 0 $.	1
8315	Find $ a_{ 67 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 0 $.	1
8316	Find $ a_{ 67 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 6 $.	1
8317	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
8318	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = \left( -1 \right) $.	1
8319	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 6 $.	1
8320	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 7 $.	1
8321	$$ a_1 = -17 ~,~ d = -1 ~,~ a_n = 72 ~,~ n = ? $$	1
8322	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 10 $.	1
8323	Find $ a_{ 72 } $ of an arithmetic progression if $ a_1 = -17 ~~ \text{and} ~~ d = 1 $.	1
8324	Find $ S_{ 292 } $ ( sum of first $ 292 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 13 $.	1
8325	Find $ S_{ 64 } $ ( sum of first $ 64 $ terms ) of arithmetic progression if $ a_1 = -48 ~~ \text{and} ~~ d = 0 $.	1
8326	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 5 $.	1
8327	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 13 $.	1
8328	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 10 $.	1
8329	Find $ S_{ 32 } $ ( sum of first $ 32 $ terms ) of arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 3 $.	1
8330	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 6 $.	1
8331	Find common difference $ d $ of arithmetic progression if $ a_1 = \frac{ 3 }{ 4 } ~~ \text{and} ~~ a_{ 2 } = \frac{ 3 }{ 16 } $.	1
8332	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = -2 $.	1
8333	Find $ S_{ 32 } $ ( sum of first $ 32 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = -3 $.	1
8334	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -\frac{ 13 }{ 8 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	1
8335	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = -\frac{ 13 }{ 8 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	1
8336	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = -\frac{ 13 }{ 8 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	1
8337	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = -\frac{ 13 }{ 8 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	1
8338	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -\frac{ 13 }{ 8 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	1
8339	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = -\frac{ 13 }{ 8 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	1
8340	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -\frac{ 13 }{ 8 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	1
8341	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 13 }{ 8 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	1
8342	Find $ S_{ 35 } $ ( sum of first $ 35 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 13 }{ 8 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	1
8343	Find $ S_{ 32 } $ ( sum of first $ 32 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 13 }{ 8 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	1
8344	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 13 }{ 8 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	1
8345	Find $ S_{ 28 } $ ( sum of first $ 28 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 13 }{ 8 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	1
8346	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 13 }{ 8 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	1
8347	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 13 }{ 8 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	1
8348	Find $ S_{ 22 } $ ( sum of first $ 22 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 13 }{ 8 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	1
8349	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 13 }{ 8 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	1
8350	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 13 }{ 8 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	1