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
751	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 8 $.	5
752	$$ a_1 = 2 ~~,~~ d = 5 ~~,~~ a_1 = ? ~~,~~ d = ? $$	5
753	$$ a_1 = 4 ~,~ d = 2 ~,~ a_n = 7 ~,~ n = ? $$	5
754	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 43 ~~ \text{and} ~~ d = \left( -7 \right) $.	5
755	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 8 $.	5
756	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $.	5
757	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -4 \right) $.	5
758	$$ a_1 = \frac{ 3 }{ 2 } ~,~ d = \frac{ 1 }{ 20 } ~,~ a_n = 20 ~,~ n = ? $$	5
759	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = -14 ~~ \text{and} ~~ d = 5 $.	5
760	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	5
761	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	5
762	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 4 $.	5
763	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \left( -2 \right) $.	5
764	Find $ a_{ 57 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 5 $.	5
765	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	5
766	Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -6 \right) $.	5
767	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 3 $.	5
768	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = -4 $.	5
769	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 334 ~~ \text{and} ~~ d = 0 $.	5
770	Find $ S_{ 3 } $ ( sum of first $ 3 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $.	5
771	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = -13 ~~ \text{and} ~~ d = \left( -11 \right) $.	5
772	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ d = \frac{ 6 }{ 5 } $.	5
773	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 319 }{ 100 } ~~ \text{and} ~~ d = \frac{ 28 }{ 25 } $.	5
774	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = \frac{ 319 }{ 100 } ~~ \text{and} ~~ d = \frac{ 28 }{ 25 } $.	5
775	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 13 $.	5
776	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 85 ~~ \text{and} ~~ d = \left( -8 \right) $.	5
777	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 85 ~~ \text{and} ~~ d = \left( -8 \right) $.	5
778	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 85 ~~ \text{and} ~~ d = \left( -8 \right) $.	5
779	Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 85 ~~ \text{and} ~~ d = -8 $.	5
780	Find $ a_{ 800 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	5
781	Find $ a_{ 750 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	5
782	Find $ a_{ 730 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	5
783	Find $ a_{ 725 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	5
784	Find $ a_{ 720 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	5
785	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -31 ~~ \text{and} ~~ d = \left( -7 \right) $.	5
786	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = -31 ~~ \text{and} ~~ d = \left( -7 \right) $.	5
787	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = -31 ~~ \text{and} ~~ d = \left( -7 \right) $.	5
788	Find $ a_{ 76 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -2 \right) $.	5
789	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	5
790	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 2 $.	5
791	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $.	5
792	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 2 $.	5
793	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 800000 ~~ \text{and} ~~ d = 750000 $.	5
794	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 750000 ~~ \text{and} ~~ d = 50000 $.	5
795	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 750000 ~~ \text{and} ~~ d = 50000 $.	5
796	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 750000 ~~ \text{and} ~~ d = 50000 $.	5
797	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 2 $.	5
798	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	5
799	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	5
800	Find $ a_1 $ (first term of arithmetic progression) if $ d = -3 ~~ \text{and} ~~ a_{ 75 } = 232 $.	5