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
551	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 1500 ~~ \text{and} ~~ d = -5 $.	6
552	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	6
553	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 6 $.	6
554	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 128 ~~ \text{and} ~~ d = 4 $.	6
555	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = -21 ~~ \text{and} ~~ d = 7 $.	6
556	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 50 $.	6
557	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 4 $.	6
558	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 65 $.	6
559	Find $ S_{ 500 } $ ( sum of first $ 500 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	6
560	Find $ S_{ 2016 } $ ( sum of first $ 2016 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	6
561	Find $ a_{ 78 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = \left( -9 \right) $.	6
562	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 18 $.	6
563	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 3 $.	6
564	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 234000 ~~ \text{and} ~~ d = 18000 $.	6
565	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 11 }{ 6 } ~~ \text{and} ~~ d = -\frac{ 3 }{ 2 } $.	6
566	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 9 $.	6
567	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 255 ~~ \text{and} ~~ d = \left( -5 \right) $.	6
568	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = -4 $.	6
569	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 5 $.	6
570	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 8 $.	6
571	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = \frac{ 3 }{ 4 } $.	6
572	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 27 ~~ \text{and} ~~ d = 5 $.	6
573	Find $ a_{ 247 } $ of an arithmetic progression if $ a_1 = 54 ~~ \text{and} ~~ d = 1 $.	6
574	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 1 $.	6
575	Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 6 $.	6
576	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = \left( -4 \right) $.	6
577	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = -4 $.	6
578	$$ a_1 = 30 ~,~ d = 5 ~,~ S_n = 500 ~,~ n = ? $$	6
579	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	6
580	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = -24 ~~ \text{and} ~~ d = 17 $.	6
581	Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = 29 ~~ \text{and} ~~ d = \left( -12 \right) $.	6
582	Find $ a_{ 95 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -9 \right) $.	6
583	$$ a_1 = 30 ~,~ d = 10 ~,~ S_n = 1500 ~,~ n = ? $$	6
584	Find $ a_{ 59 } $ of an arithmetic progression if $ a_1 = 26 ~~ \text{and} ~~ d = 9 $.	6
585	Find $ a_{ 92 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 17 $.	6
586	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 185 ~~ \text{and} ~~ d = 5 $.	6
587	Find $ a_{ 53 } $ of an arithmetic progression if $ a_1 = 27 ~~ \text{and} ~~ d = \left( -16 \right) $.	6
588	Find $ S_{ 36 } $ ( sum of first $ 36 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 3 $.	6
589	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -2 \right) $.	6
590	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $.	6
591	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 960 ~~ \text{and} ~~ d = \left( -160 \right) $.	6
592	Find $ S_{ 48 } $ ( sum of first $ 48 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 1 $.	6
593	Find $ a_{ 41 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -6 \right) $.	6
594	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	6
595	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	6
596	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 0 $.	6
597	Find $ a_{ 37 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = \frac{ 14 }{ 5 } $.	6
598	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -4 \right) $.	6
599	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 5 } ~~ \text{and} ~~ d = \frac{ 7 }{ 5 } $.	6
600	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	6