Arithmetic sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Arithmetic sequences.

Select category

ID	Problem	Count
2751	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
2752	Find $ a_{ 75 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = \left( -2 \right) $.	2
2753	Find $ a_{ 75 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = 2 $.	2
2754	Find $ S_{ 75 } $ ( sum of first $ 75 $ terms ) of arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = 2 $.	2
2755	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 9 } ~~ \text{and} ~~ d = \left( -3 \right) $.	2
2756	Find $ S_{ 93 } $ ( sum of first $ 93 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $.	2
2757	Find $ a_{ 38 } $ of an arithmetic progression if $ a_1 = 211 ~~ \text{and} ~~ d = 4 $.	2
2758	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 59 $.	2
2759	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 5 $.	2
2760	Find $ a_{ 56 } $ of an arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 5 $.	2
2761	$$ a_1 = 4 ~,~ d = -3 ~,~ S_n = -23 ~,~ n = ? $$	2
2762	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 4 } ~~ \text{and} ~~ d = \left( -1 \right) $.	2
2763	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = -3 $.	2
2764	$$ a_1 = 4 ~,~ d = -3 ~,~ a_n = -23 ~,~ n = ? $$	2
2765	$$ a_1 = 2 ~,~ d = 7 ~,~ a_n = 135 ~,~ n = ? $$	2
2766	Find $ S_{ 415 } $ ( sum of first $ 415 $ terms ) of arithmetic progression if $ a_1 = 580000 ~~ \text{and} ~~ d = 10000 $.	2
2767	$$ a_1 = 20 ~,~ d = 2 ~,~ a_n = 400 ~,~ n = ? $$	2
2768	Find $ S_{ 191 } $ ( sum of first $ 191 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 2 $.	2
2769	$$ a_{ 8 } = 19 ~~,~~ S_{ 4 } = 31 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
2770	$$ a_{ 4 } = 31 ~~,~~ S_{ 8 } = 19 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
2771	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 123 ~~ \text{and} ~~ d = 0 $.	2
2772	$$ a_1 = 2 ~,~ d = 3 ~,~ a_n = 67 ~,~ n = ? $$	2
2773	$$ a_1 = 2 ~,~ d = 3 ~,~ S_n = 67 ~,~ n = ? $$	2
2774	Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 7 $.	2
2775	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = -39 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
2776	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 100 $.	2
2777	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 219 ~~ \text{and} ~~ d = 10 $.	2
2778	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = \frac{ 43 }{ 10 } ~~ \text{and} ~~ d = -12 $.	2
2779	$$ a_1 = -11 ~,~ d = 2 ~,~ a_n = 17 ~,~ n = ? $$	2
2780	Find $ a_1 $ (first term of arithmetic progression) if $ d = 3 ~~ \text{and} ~~ a_{ 26 } = 3 $.	2
2781	Find $ S_{ 43 } $ ( sum of first $ 43 $ terms ) of arithmetic progression if $ a_1 = -72 ~~ \text{and} ~~ d = 3 $.	2
2782	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 4 $.	2
2783	Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 45 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
2784	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 45 ~~ \text{and} ~~ d = -4 $.	2
2785	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -14 ~~ \text{and} ~~ d = 4 $.	2
2786	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -14 ~~ \text{and} ~~ d = 4 $.	2
2787	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 6 $.	2
2788	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 2 $.	2
2789	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
2790	Find $ S_{ 88 } $ ( sum of first $ 88 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	2
2791	Find $ a_{ 38 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = \left( -37 \right) $.	2
2792	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 6 $.	2
2793	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
2794	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 2 $.	2
2795	Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 300 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
2796	Find $ a_{ 72 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -6 \right) $.	2
2797	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ d = \frac{ 1 }{ 100 } $.	2
2798	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	2
2799	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $.	2
2800	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 50 $.	2