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
10301	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 300 ~~ \text{and} ~~ d = \left( -80 \right) $.	1
10302	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 300 ~~ \text{and} ~~ d = \left( -80 \right) $.	1
10303	Find $ S_{ 58 } $ ( sum of first $ 58 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 1 $.	1
10304	$$ a_1 = 162 ~~,~~ d = \frac{ 1 }{ 3 } ~~,~~ a_1 = ? ~~,~~ d = ? $$	1
10305	$$ a_{ 2 } = 6 ~~,~~ S_{ 4 } = 24 ~~,~~ a_1 = ? ~~,~~ d = ? $$	1
10306	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 2 $.	1
10307	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 2 $.	1
10308	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \frac{ 21 }{ 5 } $.	1
10309	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \frac{ 21 }{ 5 } $.	1
10310	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 8 $.	1
10311	Find $ S_{ 2 } $ ( sum of first $ 2 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	1
10312	Find $ a_{ 99 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 2 $.	1
10313	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 31 ~~ \text{and} ~~ d = 21 $.	1
10314	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = \left( -4 \right) $.	1
10315	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	1
10316	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	1
10317	Find $ a_{ 43 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	1
10318	Find $ a_{ 47 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	1
10319	Find $ a_{ 48 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	1
10320	Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	1
10321	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 46 ~~ \text{and} ~~ d = \frac{ 12 }{ 5 } $.	1
10322	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 46 ~~ \text{and} ~~ d = \frac{ 12 }{ 5 } $.	1
10323	Find $ S_{ 22 } $ ( sum of first $ 22 $ terms ) of arithmetic progression if $ a_1 = 14300 ~~ \text{and} ~~ d = 100 $.	1
10324	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 14300 ~~ \text{and} ~~ d = 100 $.	1
10325	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 14300 ~~ \text{and} ~~ d = 100 $.	1
10326	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 14300 ~~ \text{and} ~~ d = 100 $.	1
10327	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 14300 ~~ \text{and} ~~ d = 100 $.	1
10328	Find $ S_{ 32 } $ ( sum of first $ 32 $ terms ) of arithmetic progression if $ a_1 = 14300 ~~ \text{and} ~~ d = 100 $.	1
10329	Find $ S_{ 32 } $ ( sum of first $ 32 $ terms ) of arithmetic progression if $ a_1 = 3500 ~~ \text{and} ~~ d = 100 $.	1
10330	Find $ S_{ 90 } $ ( sum of first $ 90 $ terms ) of arithmetic progression if $ a_1 = 3500 ~~ \text{and} ~~ d = 100 $.	1
10331	Find $ S_{ 70 } $ ( sum of first $ 70 $ terms ) of arithmetic progression if $ a_1 = 3500 ~~ \text{and} ~~ d = 100 $.	1
10332	Find $ S_{ 75 } $ ( sum of first $ 75 $ terms ) of arithmetic progression if $ a_1 = 3500 ~~ \text{and} ~~ d = 100 $.	1
10333	Find $ S_{ 72 } $ ( sum of first $ 72 $ terms ) of arithmetic progression if $ a_1 = 3500 ~~ \text{and} ~~ d = 100 $.	1
10334	Find $ S_{ 73 } $ ( sum of first $ 73 $ terms ) of arithmetic progression if $ a_1 = 3500 ~~ \text{and} ~~ d = 100 $.	1
10335	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 10800 ~~ \text{and} ~~ d = 100 $.	1
10336	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 10800 ~~ \text{and} ~~ d = 100 $.	1
10337	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 10800 ~~ \text{and} ~~ d = 100 $.	1
10338	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 10800 ~~ \text{and} ~~ d = 100 $.	1
10339	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 4100 ~~ \text{and} ~~ d = 100 $.	1
10340	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 4100 ~~ \text{and} ~~ d = 100 $.	1
10341	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 4100 ~~ \text{and} ~~ d = 100 $.	1
10342	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 4100 ~~ \text{and} ~~ d = 100 $.	1
10343	Find $ S_{ 22 } $ ( sum of first $ 22 $ terms ) of arithmetic progression if $ a_1 = 4100 ~~ \text{and} ~~ d = 100 $.	1
10344	Find $ a_{ 58 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 8 $.	1
10345	Find $ a_{ 43 } $ of an arithmetic progression if $ a_1 = 66743 ~~ \text{and} ~~ d = 7 $.	1
10346	Find $ a_{ 77 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 8 $.	1
10347	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 31 ~~ \text{and} ~~ d = 8 $.	1
10348	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -\frac{ 2 }{ 3 } \right) $.	1
10349	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 7 $.	1
10350	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $.	1