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
3551	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	2
3552	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	2
3553	Find $ a_{ 81 } $ of an arithmetic progression if $ a_1 = 156 ~~ \text{and} ~~ d = 23 $.	2
3554	Find $ S_{ 81 } $ ( sum of first $ 81 $ terms ) of arithmetic progression if $ a_1 = 156 ~~ \text{and} ~~ d = 23 $.	2
3555	Find $ a_{ 10000 } $ of an arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 500 $.	2
3556	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 500 $.	2
3557	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = 9 $.	2
3558	Find $ a_{ 74 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 0 $.	2
3559	Find $ S_{ 900 } $ ( sum of first $ 900 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 9 $.	2
3560	$$ a_1 = 16 ~,~ d = -3 ~,~ a_n = -6 ~,~ n = ? $$	2
3561	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 7 $.	2
3562	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 2 $.	2
3563	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 2 $.	2
3564	Find $ S_{ 78 } $ ( sum of first $ 78 $ terms ) of arithmetic progression if $ a_1 = 77 ~~ \text{and} ~~ d = 2 $.	2
3565	Find $ a_{ 78 } $ of an arithmetic progression if $ a_1 = 77 ~~ \text{and} ~~ d = 2 $.	2
3566	Find $ a_{ 79 } $ of an arithmetic progression if $ a_1 = 77 ~~ \text{and} ~~ d = 2 $.	2
3567	Find $ S_{ 79 } $ ( sum of first $ 79 $ terms ) of arithmetic progression if $ a_1 = 77 ~~ \text{and} ~~ d = 2 $.	2
3568	Find $ d $ (common difference of arithmetic progression) if $ a_1 = 9 ~~ \text{and} ~~ S_{ 20 } = 1320 $.	2
3569	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \frac{ 333 }{ 100 } $.	2
3570	Find $ S_{ 44 } $ ( sum of first $ 44 $ terms ) of arithmetic progression if $ a_1 = 39 ~~ \text{and} ~~ d = 4 $.	2
3571	$$ a_1 = 19 ~,~ d = 1 ~,~ a_n = 30 ~,~ n = ? $$	2
3572	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 1 $.	2
3573	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 1 $.	2
3574	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 54000 ~~ \text{and} ~~ d = 1600 $.	2
3575	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -14 \right) $.	2
3576	Find $ a_{ 47 } $ of an arithmetic progression if $ a_1 = \frac{ 51 }{ 10 } ~~ \text{and} ~~ d = \frac{ 3 }{ 10 } $.	2
3577	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 3 $.	2
3578	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = \left( -1 \right) $.	2
3579	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	2
3580	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 32000 ~~ \text{and} ~~ d = \left( -\frac{ 3 }{ 50 } \right) $.	2
3581	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 180 ~~ \text{and} ~~ d = \left( -50 \right) $.	2
3582	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
3583	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $.	2
3584	$$ a_1 = 200 ~,~ d = -10 ~,~ a_n = 20 ~,~ n = ? $$	2
3585	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 7 $.	2
3586	Find $ a_{ 2000 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 0 $.	2
3587	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = \frac{ 47 }{ 10 } ~~ \text{and} ~~ d = \left( -2 \right) $.	2
3588	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = 1 $.	2
3589	Find common difference $ d $ of arithmetic progression if $ a_1 = \frac{ 3 }{ 4 } ~~ \text{and} ~~ a_{ 2 } = \frac{ 5 }{ 8 } $.	2
3590	Find $ a_{ 88 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
3591	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = \frac{ 2 }{ 5 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	2
3592	Find $ S_{ 2023 } $ ( sum of first $ 2023 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	2
3593	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = \left( -\frac{ 3 }{ 2 } \right) $.	2
3594	Find $ S_{ 1000 } $ ( sum of first $ 1000 $ terms ) of arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 33 $.	2
3595	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 300 $.	2
3596	$$ a_1 = 0 ~,~ d = 4 ~,~ a_n = 3 ~,~ n = ? $$	2
3597	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 41600 ~~ \text{and} ~~ d = 1560 $.	2
3598	Find $ S_{ 192 } $ ( sum of first $ 192 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	2
3599	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
3600	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	2