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
4701	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 60000 ~~ \text{and} ~~ d = 3000 $.	2
4702	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \frac{ 1 }{ 5 } $.	2
4703	Find $ S_{ 99 } $ ( sum of first $ 99 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 12 $.	2
4704	Find $ a_{ 65 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 74 $.	2
4705	Find $ S_{ 163 } $ ( sum of first $ 163 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ d = \frac{ 1 }{ 100 } $.	2
4706	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	2
4707	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 1 $.	2
4708	Find $ a_{ 53 } $ of an arithmetic progression if $ a_1 = 76 ~~ \text{and} ~~ d = 8 $.	2
4709	Find $ a_{ 87 } $ of an arithmetic progression if $ a_1 = 49 ~~ \text{and} ~~ d = \left( -13 \right) $.	2
4710	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = 4 $.	2
4711	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 0 $.	2
4712	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 98 ~~ \text{and} ~~ d = 0 $.	2
4713	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = 0 $.	2
4714	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = 1 $.	2
4715	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = -20 ~~ \text{and} ~~ d = 7 $.	2
4716	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 4 $.	2
4717	Find $ S_{ 86 } $ ( sum of first $ 86 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
4718	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \left( -8 \right) $.	2
4719	Find $ a_{ 61 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 3 $.	2
4720	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 20 $.	2
4721	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $.	2
4722	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
4723	Find $ a_{ 37 } $ of an arithmetic progression if $ a_1 = 412 ~~ \text{and} ~~ d = \left( -8 \right) $.	2
4724	Find $ a_{ 43 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 4 $.	2
4725	$$ a_1 = 9375 ~,~ d = \frac{ 5 }{ 4 } ~,~ a_n = 8 ~,~ n = ? $$	2
4726	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 7 $.	2
4727	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
4728	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 25 $.	2
4729	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
4730	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 2 $.	2
4731	Find $ a_{ 83 } $ of an arithmetic progression if $ a_1 = 1001 ~~ \text{and} ~~ d = 1 $.	2
4732	$$ a_1 = 1001 ~,~ d = 1 ~,~ a_n = 1083 ~,~ n = ? $$	2
4733	Find $ S_{ 83 } $ ( sum of first $ 83 $ terms ) of arithmetic progression if $ a_1 = 1001 ~~ \text{and} ~~ d = 1 $.	2
4734	$$ a_1 = 19 ~,~ d = 19 ~,~ a_n = 988 ~,~ n = ? $$	2
4735	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 2 $.	2
4736	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 5 $.	2
4737	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	2
4738	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ d = \frac{ 9 }{ 4 } $.	2
4739	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 2 }{ 5 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
4740	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 3 } \right) $.	2
4741	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = -50 ~~ \text{and} ~~ d = 15 $.	2
4742	$$ a_1 = -21 ~~,~~ d = \frac{ 5 }{ 6 } ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
4743	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ d = 0 $.	2
4744	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	2
4745	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = \left( -\frac{ 7 }{ 2 } \right) $.	2
4746	Find $ S_{ 48 } $ ( sum of first $ 48 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 6 $.	2
4747	Find $ a_{ 249 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	2
4748	Find $ S_{ 249 } $ ( sum of first $ 249 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	2
4749	Find $ S_{ 89 } $ ( sum of first $ 89 $ terms ) of arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 4 $.	2
4750	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 300000 ~~ \text{and} ~~ d = 0 $.	2