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
10401	Find $ S_{ 300 } $ ( sum of first $ 300 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \frac{ 3 }{ 5 } $.	1
10402	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = -5 $.	1
10403	Find $ a_{ 69 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	1
10404	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
10405	$$ a_1 = 16 ~,~ d = \frac{ 1 }{ 5 } ~,~ a_n = 25 ~,~ n = ? $$	1
10406	Find $ S_{ 46 } $ ( sum of first $ 46 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = \frac{ 1 }{ 5 } $.	1
10407	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 2 $.	1
10408	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $.	1
10409	Find $ S_{ 64 } $ ( sum of first $ 64 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	1
10410	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 0 $.	1
10411	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 6 $.	1
10412	Find $ a_{ 71 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 6 $.	1
10413	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	1
10414	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
10415	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \frac{ 1 }{ 5 } $.	1
10416	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $.	1
10417	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = \left( -1 \right) $.	1
10418	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = -6 $.	1
10419	$$ a_1 = 12 ~,~ a_n = 308 ~,~ S_n = 6080 ~,~ n = ? $$	1
10420	Find $ a_{ 45 } $ of an arithmetic progression if $ a_1 = 775 ~~ \text{and} ~~ d = 12 $.	1
10421	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 250 ~~ \text{and} ~~ d = 15 $.	1
10422	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 5 $.	1
10423	$$ a_1 = 1 ~~,~~ d = 2 ~~,~~ a_1 = ? ~~,~~ d = ? $$	1
10424	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	1
10425	Find $ S_{ 52 } $ ( sum of first $ 52 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	1
10426	Find $ S_{ 52 } $ ( sum of first $ 52 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	1
10427	Find $ S_{ 52 } $ ( sum of first $ 52 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	1
10428	Find $ S_{ 52 } $ ( sum of first $ 52 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ d = \frac{ 1 }{ 100 } $.	1
10429	Find $ a_{ 99 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	1
10430	Find $ S_{ 52 } $ ( sum of first $ 52 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	1
10431	Find $ S_{ 520 } $ ( sum of first $ 520 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	1
10432	Find $ S_{ 365 } $ ( sum of first $ 365 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	1
10433	Find $ S_{ 365 } $ ( sum of first $ 365 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	1
10434	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	1
10435	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	1
10436	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	1
10437	Find $ S_{ 43 } $ ( sum of first $ 43 $ terms ) of arithmetic progression if $ a_1 = -121 ~~ \text{and} ~~ d = 3 $.	1
10438	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 84 $.	1
10439	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 1234567 ~~ \text{and} ~~ d = 0 $.	1
10440	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 6 $.	1
10441	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = \frac{ 7 }{ 2 } ~~ \text{and} ~~ d = \frac{ 7 }{ 2 } $.	1
10442	Find $ S_{ 300000 } $ ( sum of first $ 300000 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	1
10443	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 0 $.	1
10444	Find $ a_{ 90 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $.	1
10445	Find $ a_{ 36 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 0 $.	1
10446	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	1
10447	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 6 $.	1
10448	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 6 $.	1
10449	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 4 $.	1
10450	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 200 $.	1