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
3451	$$ a_1 = 1 ~,~ d = 6 ~,~ a_n = 12 ~,~ n = ? $$	2
3452	Find $ S_{ 1000 } $ ( sum of first $ 1000 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 8 $.	2
3453	Find $ S_{ 2609 } $ ( sum of first $ 2609 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
3454	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = -5 $.	2
3455	Find $ S_{ 106 } $ ( sum of first $ 106 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 2 $.	2
3456	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	2
3457	Find $ a_{ 45 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 3 $.	2
3458	Find $ a_{ 300 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	2
3459	Find $ S_{ 300 } $ ( sum of first $ 300 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
3460	Find $ a_{ 48 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	2
3461	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 5 $.	2
3462	$$ a_1 = 33 ~,~ d = 1 ~,~ a_n = 533 ~,~ n = ? $$	2
3463	$$ a_1 = 22 ~,~ d = -3 ~,~ a_n = 38 ~,~ n = ? $$	2
3464	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	2
3465	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 54 ~~ \text{and} ~~ d = 5 $.	2
3466	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 3 $.	2
3467	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 40000 ~~ \text{and} ~~ d = 3000 $.	2
3468	Find $ a_{ 119 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	2
3469	Find $ S_{ 38 } $ ( sum of first $ 38 $ terms ) of arithmetic progression if $ a_1 = -30 ~~ \text{and} ~~ d = 19 $.	2
3470	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = 10 $.	2
3471	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
3472	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
3473	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = \left( -\frac{ 33 }{ 4 } \right) $.	2
3474	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
3475	$$ d = 8 ~,~ a_n = 13 ~,~ S_n = 1222 ~,~ n = ? $$	2
3476	Find $ a_1 $ (first term of arithmetic progression) if $ d = 3 ~~ \text{and} ~~ S_{ 14 } = 581 $.	2
3477	Find $ d $ (common difference of arithmetic progression) if $ a_1 = -90 ~~ \text{and} ~~ S_{ 31 } = 3255 $.	2
3478	Find $ d $ (common difference of arithmetic progression) if $ a_1 = 257 ~~ \text{and} ~~ S_{ 32 } = 3264 $.	2
3479	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = -70 ~~ \text{and} ~~ d = 9 $.	2
3480	$$ a_1 = 74 ~,~ d = 3 ~,~ a_n = 84 ~,~ n = ? $$	2
3481	Find $ a_{ 84 } $ of an arithmetic progression if $ a_1 = 74 ~~ \text{and} ~~ d = 3 $.	2
3482	Find $ a_{ 445 } $ of an arithmetic progression if $ a_1 = -22 ~~ \text{and} ~~ d = 2 $.	2
3483	Find $ S_{ 46 } $ ( sum of first $ 46 $ terms ) of arithmetic progression if $ a_1 = 22 ~~ \text{and} ~~ d = 3 $.	2
3484	Find $ S_{ 35 } $ ( sum of first $ 35 $ terms ) of arithmetic progression if $ a_1 = -58 ~~ \text{and} ~~ d = 12 $.	2
3485	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 660 ~~ \text{and} ~~ d = 5 $.	2
3486	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 173 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
3487	Find $ S_{ 60 } $ ( sum of first $ 60 $ terms ) of arithmetic progression if $ a_1 = 173 ~~ \text{and} ~~ d = -2 $.	2
3488	Find $ a_{ 48 } $ of an arithmetic progression if $ a_1 = 26 ~~ \text{and} ~~ d = 4 $.	2
3489	Find $ S_{ 48 } $ ( sum of first $ 48 $ terms ) of arithmetic progression if $ a_1 = 26 ~~ \text{and} ~~ d = 4 $.	2
3490	Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 50 } ~~ \text{and} ~~ d = \frac{ 1 }{ 50 } $.	2
3491	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 50 } ~~ \text{and} ~~ d = 2 $.	2
3492	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 16 $.	2
3493	Find $ a_{ 39 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 5 $.	2
3494	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $.	2
3495	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
3496	Find $ a_{ 62 } $ of an arithmetic progression if $ a_1 = 89 ~~ \text{and} ~~ d = 8 $.	2
3497	$$ a_{ 40 } = 144 ~~,~~ S_{ 40 } = 2640 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
3498	$$ a_{ 6 } = 21 ~~,~~ S_{ 17 } = 0 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
3499	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = \left( -10 \right) $.	2
3500	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = 8 $.	2