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
7301	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -40 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
7302	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -22 ~~ \text{and} ~~ d = 100 $.	1
7303	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 10 $.	1
7304	Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = -21 ~~ \text{and} ~~ d = 6 $.	1
7305	Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = \left( -10 \right) $.	1
7306	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 38 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
7307	Find $ a_{ 37 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
7308	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	1
7309	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	1
7310	Find $ S_{ 52 } $ ( sum of first $ 52 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = -5 $.	1
7311	Find $ a_{ 782 } $ of an arithmetic progression if $ a_1 = 9999 ~~ \text{and} ~~ d = 9999 $.	1
7312	Find $ S_{ 782 } $ ( sum of first $ 782 $ terms ) of arithmetic progression if $ a_1 = 9999 ~~ \text{and} ~~ d = 9999 $.	1
7313	Find $ a_{ 38 } $ of an arithmetic progression if $ a_1 = -40 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
7314	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 200 $.	1
7315	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = -35 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
7316	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = \left( -15 \right) $.	1
7317	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 6 $.	1
7318	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 4 $.	1
7319	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 4 $.	1
7320	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 6 $.	1
7321	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 6 $.	1
7322	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 2 $.	1
7323	Find $ S_{ 45 } $ ( sum of first $ 45 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $.	1
7324	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 7 $.	1
7325	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -52 ~~ \text{and} ~~ d = 11 $.	1
7326	$$ a_1 = -52 ~~,~~ d = 11 ~~,~~ a_1 = ? ~~,~~ d = ? $$	1
7327	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \frac{ 11 }{ 10 } $.	1
7328	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	1
7329	Find $ a_{ 99 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	1
7330	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	1
7331	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 36 ~~ \text{and} ~~ d = 0 $.	1
7332	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = \frac{ 9 }{ 2 } ~~ \text{and} ~~ d = \frac{ 3 }{ 4 } $.	1
7333	Find $ a_{ 71 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	1
7334	Find $ S_{ 70 } $ ( sum of first $ 70 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 1000 $.	1
7335	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 1000 $.	1
7336	$$ a_1 = 36 ~,~ d = -\frac{ 2 }{ 3 } ~,~ a_n = -30 ~,~ n = ? $$	1
7337	$$ a_1 = 1024 ~,~ d = 1024 ~,~ a_n = 9 ~,~ n = ? $$	1
7338	Find $ S_{ 35 } $ ( sum of first $ 35 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	1
7339	Find $ S_{ 39 } $ ( sum of first $ 39 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $.	1
7340	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -13 ~~ \text{and} ~~ d = 4 $.	1
7341	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	1
7342	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 8300 ~~ \text{and} ~~ d = 200 $.	1
7343	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 8300 ~~ \text{and} ~~ d = 200 $.	1
7344	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 250 $.	1
7345	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 128 ~~ \text{and} ~~ d = \frac{ 271 }{ 50 } $.	1
7346	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 128 ~~ \text{and} ~~ d = \frac{ 271 }{ 50 } $.	1
7347	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 6 $.	1
7348	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 1400 ~~ \text{and} ~~ d = 200 $.	1
7349	Find $ a_{ 57 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 33 $.	1
7350	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 0 $.	1