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
6301	Find $ S_{ 39 } $ ( sum of first $ 39 $ terms ) of arithmetic progression if $ a_1 = 116 ~~ \text{and} ~~ d = -6 $.	1
6302	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 1000 $.	1
6303	Find $ S_{ 300 } $ ( sum of first $ 300 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 250 $.	1
6304	Find $ S_{ 150 } $ ( sum of first $ 150 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 250 $.	1
6305	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = -5 $.	1
6306	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
6307	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 6700000 ~~ \text{and} ~~ d = 100000 $.	1
6308	$$ a_1 = 7 ~,~ d = -3 ~,~ a_n = -296 ~,~ n = ? $$	1
6309	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 20 $.	1
6310	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -4 \right) $.	1
6311	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = -5 $.	1
6312	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
6313	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 8 $.	1
6314	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 2 $.	1
6315	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 5 $.	1
6316	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 34 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
6317	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	1
6318	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 25000 ~~ \text{and} ~~ d = 1600 $.	1
6319	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 7 $.	1
6320	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 7 $.	1
6321	$$ a_1 = 2 ~,~ d = 5 ~,~ a_n = 44 ~,~ n = ? $$	1
6322	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $.	1
6323	Find $ a_1 $ (first term of arithmetic progression) if $ d = 6 ~~ \text{and} ~~ a_{ 101 } = 596 $.	1
6324	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 6 $.	1
6325	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 6 $.	1
6326	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 3 $.	1
6327	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 3 $.	1
6328	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = \left( -7 \right) $.	1
6329	Find $ S_{ 365 } $ ( sum of first $ 365 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 364 $.	1
6330	Find $ a_{ 43 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	1
6331	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 9 $.	1
6332	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 6 $.	1
6333	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 10 } ~~ \text{and} ~~ d = \frac{ 1 }{ 20 } $.	1
6334	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 10 } ~~ \text{and} ~~ d = \frac{ 1 }{ 20 } $.	1
6335	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 7 $.	1
6336	Find $ S_{ 98 } $ ( sum of first $ 98 $ terms ) of arithmetic progression if $ a_1 = 42 ~~ \text{and} ~~ d = 1 $.	1
6337	Find $ S_{ 1000 } $ ( sum of first $ 1000 $ terms ) of arithmetic progression if $ a_1 = 2000 ~~ \text{and} ~~ d = 200 $.	1
6338	Find $ S_{ 1 } $ ( sum of first $ 1 $ terms ) of arithmetic progression if $ a_1 = 9245 ~~ \text{and} ~~ d = 5429 $.	1
6339	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 9245 ~~ \text{and} ~~ d = 5736 $.	1
6340	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -36 ~~ \text{and} ~~ d = 7 $.	1
6341	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 7 $.	1
6342	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 37 ~~ \text{and} ~~ d = 8 $.	1
6343	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 6 $.	1
6344	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 50 $.	1
6345	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 7 $.	1
6346	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = \frac{ 4 }{ 5 } $.	1
6347	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = \left( -9 \right) $.	1
6348	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $.	1
6349	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 3750 ~~ \text{and} ~~ d = 5 $.	1
6350	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 3750 ~~ \text{and} ~~ d = 5 $.	1