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
5551	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 7 $.	2
5552	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 11 $.	2
5553	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 21 $.	2
5554	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 7 $.	2
5555	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	2
5556	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
5557	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 0 $.	2
5558	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 6 $.	2
5559	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 36 ~~ \text{and} ~~ d = 8 $.	2
5560	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = \left( -9 \right) $.	2
5561	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 29 ~~ \text{and} ~~ d = 9 $.	2
5562	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 34 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
5563	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 20 $.	2
5564	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = -13 ~~ \text{and} ~~ d = 2 $.	2
5565	Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 3 $.	2
5566	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 22 ~~ \text{and} ~~ d = 0 $.	2
5567	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 1 $.	2
5568	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = -64 ~~ \text{and} ~~ d = 8 $.	2
5569	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = -22 ~~ \text{and} ~~ d = 0 $.	2
5570	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 12 $.	2
5571	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 48 ~~ \text{and} ~~ d = 0 $.	2
5572	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \left( -1 \right) $.	2
5573	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 4 $.	2
5574	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = -13 ~~ \text{and} ~~ d = 11 $.	2
5575	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \left( -\frac{ 2 }{ 3 } \right) $.	2
5576	Find $ a_{ 84 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
5577	Find $ a_{ 51 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 5 $.	2
5578	Find $ a_{ 65 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 1 $.	2
5579	Find $ a_{ 81 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 5 $.	2
5580	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = -14 ~~ \text{and} ~~ d = 3 $.	2
5581	Find $ a_{ 97 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = \left( -1 \right) $.	2
5582	Find $ a_{ 51 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
5583	Find $ a_{ 83 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
5584	Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
5585	Find $ S_{ 60 } $ ( sum of first $ 60 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 6 $.	2
5586	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = \frac{ 21 }{ 5 } ~~ \text{and} ~~ d = \left( -5 \right) $.	2
5587	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 9 $.	2
5588	Find $ S_{ 999 } $ ( sum of first $ 999 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
5589	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
5590	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
5591	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 27 ~~ \text{and} ~~ d = 27 $.	2
5592	$$ a_1 = 27 ~,~ d = 27 ~,~ a_n = 540 ~,~ n = ? $$	2
5593	Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 6 $.	2
5594	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 5 } ~~ \text{and} ~~ d = \left( -1 \right) $.	2
5595	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 55000 ~~ \text{and} ~~ d = 650 $.	2
5596	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 55000 ~~ \text{and} ~~ d = 650 $.	2
5597	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
5598	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	2
5599	$$ a_1 = 1 ~~,~~ d = -3 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
5600	Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 6 $.	2