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
601	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 6 $.	6
602	Find $ a_{ 39 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = \left( -6 \right) $.	6
603	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 7 $.	6
604	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 0 $.	6
605	Find $ a_{ 94 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 6 $.	6
606	Find $ S_{ 200 } $ ( sum of first $ 200 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 7 $.	6
607	Find $ a_1 $ (first term of arithmetic progression) if $ d = 3 ~~ \text{and} ~~ a_{ 3 } = 15 $.	6
608	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	6
609	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 6 $.	6
610	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 3 $.	6
611	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 4 $.	6
612	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	6
613	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 3 $.	6
614	Find $ a_1 $ (first term of arithmetic progression) if $ d = 3 ~~ \text{and} ~~ a_{ 5 } = 40 $.	6
615	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 2 $.	6
616	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $.	6
617	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 4 $.	6
618	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	6
619	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = \frac{ 9 }{ 4 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $.	6
620	$$ a_1 = 5 ~~,~~ d = 5 ~~,~~ a_1 = ? ~~,~~ d = ? $$	6
621	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = \left( -3 \right) $.	6
622	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 1 $.	6
623	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	6
624	Find $ S_{ 336 } $ ( sum of first $ 336 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 20 $.	6
625	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 7 $.	6
626	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 5 $.	6
627	Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 13 $.	6
628	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 45 ~~ \text{and} ~~ d = 3 $.	6
629	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 3 $.	6
630	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -5 \right) $.	6
631	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 20 $.	6
632	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = -1 $.	6
633	Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 4 $.	6
634	Find $ S_{ 46 } $ ( sum of first $ 46 $ terms ) of arithmetic progression if $ a_1 = \frac{ 6 }{ 5 } ~~ \text{and} ~~ d = \frac{ 3 }{ 5 } $.	6
635	Find $ a_{ 90 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	6
636	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = -6 $.	6
637	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \frac{ 11 }{ 2 } $.	6
638	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	6
639	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 96 ~~ \text{and} ~~ d = 94 $.	6
640	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	6
641	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	6
642	Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	6
643	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	6
644	Find $ a_{ 41 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 9 $.	6
645	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	6
646	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 20 $.	6
647	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	6
648	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 47 }{ 160 } $.	6
649	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	6
650	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 2 $.	6