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
4401	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $.	2
4402	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 56 ~~ \text{and} ~~ d = -4 $.	2
4403	Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = 22 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
4404	Find $ a_{ 90 } $ of an arithmetic progression if $ a_1 = -50 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
4405	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 2 $.	2
4406	Find $ a_{ 47 } $ of an arithmetic progression if $ a_1 = 310 ~~ \text{and} ~~ d = \left( -6 \right) $.	2
4407	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
4408	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 3 $.	2
4409	Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = 79158237316 ~~ \text{and} ~~ d = 0 $.	2
4410	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
4411	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 30000 ~~ \text{and} ~~ d = 2250 $.	2
4412	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 2 $.	2
4413	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	2
4414	Find $ S_{ 101 } $ ( sum of first $ 101 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	2
4415	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	2
4416	Find $ a_{ 84 } $ of an arithmetic progression if $ a_1 = -1286 ~~ \text{and} ~~ d = 17 $.	2
4417	Find $ a_{ 97 } $ of an arithmetic progression if $ a_1 = 639 ~~ \text{and} ~~ d = \left( -8 \right) $.	2
4418	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = 0 $.	2
4419	Find $ S_{ 82 } $ ( sum of first $ 82 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 4 $.	2
4420	Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = -17 ~~ \text{and} ~~ d = 20 $.	2
4421	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = -30 ~~ \text{and} ~~ d = \left( -100 \right) $.	2
4422	Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = -35 ~~ \text{and} ~~ d = 2 $.	2
4423	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 7 $.	2
4424	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
4425	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 14300 ~~ \text{and} ~~ d = 100 $.	2
4426	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 14300 ~~ \text{and} ~~ d = 100 $.	2
4427	Find $ a_{ 1000 } $ of an arithmetic progression if $ a_1 = 171 ~~ \text{and} ~~ d = 256 $.	2
4428	$$ a_1 = 16 ~,~ d = 16 ~,~ a_n = 224 ~,~ n = ? $$	2
4429	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 16 $.	2
4430	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 4 $.	2
4431	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 386 ~~ \text{and} ~~ d = 72 $.	2
4432	Find $ S_{ 20000 } $ ( sum of first $ 20000 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $.	2
4433	Find $ S_{ 1 } $ ( sum of first $ 1 $ terms ) of arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 3 $.	2
4434	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 300 ~~ \text{and} ~~ d = \left( -80 \right) $.	2
4435	Find $ S_{ 57 } $ ( sum of first $ 57 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 1 $.	2
4436	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 8 $.	2
4437	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 2 $.	2
4438	Find common difference $ d $ of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ a_{ 6 } = 24 $.	2
4439	Find $ S_{ 1010 } $ ( sum of first $ 1010 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
4440	Find $ S_{ 3 } $ ( sum of first $ 3 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	2
4441	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = -4 $.	2
4442	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = -5 $.	2
4443	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	2
4444	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = -25 ~~ \text{and} ~~ d = 9 $.	2
4445	Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 9 $.	2
4446	Find $ S_{ 378 } $ ( sum of first $ 378 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
4447	Find $ S_{ 200 } $ ( sum of first $ 200 $ terms ) of arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 5 $.	2
4448	Find $ S_{ 47 } $ ( sum of first $ 47 $ terms ) of arithmetic progression if $ a_1 = 169 ~~ \text{and} ~~ d = -8 $.	2
4449	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $.	2
4450	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = \left( -\frac{ 5 }{ 2 } \right) $.	2