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
651	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 27 ~~ \text{and} ~~ d = \left( -5 \right) $.	6
652	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 8 $.	6
653	Find $ a_{ 88 } $ of an arithmetic progression if $ a_1 = 26 ~~ \text{and} ~~ d = 2 $.	6
654	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	6
655	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	6
656	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	6
657	Find $ a_{ 99 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 6 $.	6
658	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 4 $.	6
659	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	6
660	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 3 $.	6
661	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 0 $.	6
662	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 2 $.	6
663	Find $ S_{ 45 } $ ( sum of first $ 45 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $.	6
664	Find $ a_{ 56 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	6
665	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $.	6
666	$$ a_1 = 46 ~,~ d = -11 ~,~ a_n = -20 ~,~ n = ? $$	6
667	Find $ a_{ 2500 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 190 $.	6
668	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \frac{ 29 }{ 12 } $.	6
669	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 26 ~~ \text{and} ~~ d = \left( -9 \right) $.	6
670	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	6
671	$$ a_1 = 72 ~,~ d = 1 ~,~ a_n = 190 ~,~ n = ? $$	6
672	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 13 $.	6
673	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 41 ~~ \text{and} ~~ d = \left( -10 \right) $.	6
674	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 360 ~~ \text{and} ~~ d = \left( -17 \right) $.	6
675	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = \frac{ 11 }{ 10 } ~~ \text{and} ~~ d = \frac{ 11 }{ 10 } $.	6
676	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = \frac{ 11 }{ 10 } ~~ \text{and} ~~ d = \frac{ 11 }{ 10 } $.	6
677	Find $ S_{ 99 } $ ( sum of first $ 99 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	6
678	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	5
679	Find $ S_{ 39 } $ ( sum of first $ 39 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 5 $.	5
680	Find $ S_{ 200 } $ ( sum of first $ 200 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 5 $.	5
681	Find $ a_1 $ (first term of arithmetic progression) if $ d = 4 ~~ \text{and} ~~ a_{ 32 } = 640 $.	5
682	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 5 $.	5
683	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 5 $.	5
684	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $.	5
685	Find $ a_1 $ (first term of arithmetic progression) if $ d = 4 ~~ \text{and} ~~ a_{ 4 } = 10 $.	5
686	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = -\frac{ 5 }{ 2 } $.	5
687	Find $ a_{ 2059 } $ of an arithmetic progression if $ a_1 = 5920 ~~ \text{and} ~~ d = 9205 $.	5
688	Find $ a_{ 61 } $ of an arithmetic progression if $ a_1 = -13 ~~ \text{and} ~~ d = 2 $.	5
689	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 7 $.	5
690	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = \left( -2 \right) $.	5
691	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = \left( -3 \right) $.	5
692	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = -2 $.	5
693	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 7 $.	5
694	Find $ S_{ 22 } $ ( sum of first $ 22 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 8 $.	5
695	Find $ a_{ 47 } $ of an arithmetic progression if $ a_1 = 361 ~~ \text{and} ~~ d = \left( -7 \right) $.	5
696	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -35 ~~ \text{and} ~~ d = \left( -23 \right) $.	5
697	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $.	5
698	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 225 ~~ \text{and} ~~ d = 29 $.	5
699	Find $ a_{ 61 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 7 $.	5
700	Find $ S_{ 302 } $ ( sum of first $ 302 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 3 $.	5