Arithmetic sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Arithmetic sequences.

Select category

ID	Problem	Count
4501	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 6 $.	2
4502	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $.	2
4503	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 2 $.	2
4504	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
4505	Find $ S_{ 400 } $ ( sum of first $ 400 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $.	2
4506	Find $ a_{ 26 } $ of an arithmetic progression if $ a_1 = -\frac{ 1467 }{ 25 } ~~ \text{and} ~~ d = \frac{ 833 }{ 50 } $.	2
4507	Find $ S_{ 75 } $ ( sum of first $ 75 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 100 $.	2
4508	Find $ S_{ 75 } $ ( sum of first $ 75 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 200 $.	2
4509	Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	2
4510	Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 4 $.	2
4511	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 0 $.	2
4512	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
4513	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
4514	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
4515	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = -3 $.	2
4516	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 5000 ~~ \text{and} ~~ d = 8000 $.	2
4517	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
4518	Find $ a_{ 37 } $ of an arithmetic progression if $ a_1 = 249 ~~ \text{and} ~~ d = 8 $.	2
4519	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 120 $.	2
4520	Find $ S_{ 60 } $ ( sum of first $ 60 $ terms ) of arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $.	2
4521	Find $ a_{ 87 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 7 $.	2
4522	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 4 $.	2
4523	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 1200 ~~ \text{and} ~~ d = -7 $.	2
4524	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 3 $.	2
4525	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 5 $.	2
4526	Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 5 $.	2
4527	Find $ S_{ 2 } $ ( sum of first $ 2 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	2
4528	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 1 $.	2
4529	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 0 $.	2
4530	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 10 $.	2
4531	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
4532	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = -11 $.	2
4533	Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = -6 $.	2
4534	Find $ S_{ 300 } $ ( sum of first $ 300 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
4535	Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 8 $.	2
4536	$$ a_1 = 3 ~,~ d = 3 ~,~ a_n = 19 ~,~ n = ? $$	2
4537	Find $ S_{ 360 } $ ( sum of first $ 360 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	2
4538	Find $ S_{ 71 } $ ( sum of first $ 71 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	2
4539	Find $ a_{ 66 } $ of an arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = 4 $.	2
4540	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 150 ~~ \text{and} ~~ d = 6 $.	2
4541	Find $ S_{ 41 } $ ( sum of first $ 41 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 6 $.	2
4542	Find $ a_{ 44 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 7 $.	2
4543	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 0 $.	2
4544	$$ a_{ 8 } = 14 ~~,~~ S_{ 11 } = 35 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
4545	$$ a_1 = 1 ~,~ d = \frac{ 3 }{ 2 } ~,~ a_n = 52 ~,~ n = ? $$	2
4546	Find $ S_{ 35 } $ ( sum of first $ 35 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 200 $.	2
4547	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 200 $.	2
4548	Find $ S_{ 32 } $ ( sum of first $ 32 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 200 $.	2
4549	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 164 ~~ \text{and} ~~ d = \left( -16 \right) $.	2
4550	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 75 ~~ \text{and} ~~ d = 25 $.	2