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
2951	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = -\frac{ 14 }{ 5 } $.	2
2952	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = -20 ~~ \text{and} ~~ d = \left( -\frac{ 36 }{ 5 } \right) $.	2
2953	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = \left( -\frac{ 2 }{ 3 } \right) $.	2
2954	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ d = \frac{ 1 }{ 5 } $.	2
2955	Find $ a_{ 37 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
2956	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ d = \left( -2 \right) $.	2
2957	Find $ a_{ 42 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 6 $.	2
2958	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 7 $.	2
2959	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
2960	Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = 2 $.	2
2961	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 91 }{ 10 } ~~ \text{and} ~~ d = \left( -\frac{ 8 }{ 5 } \right) $.	2
2962	Find $ a_{ 47 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
2963	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 8 $.	2
2964	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 11 $.	2
2965	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 300 $.	2
2966	Find $ S_{ 1008 } $ ( sum of first $ 1008 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	2
2967	Find $ a_{ 63 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 7 $.	2
2968	Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 0 $.	2
2969	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 101 ~~ \text{and} ~~ d = 1 $.	2
2970	Find $ S_{ 400 } $ ( sum of first $ 400 $ terms ) of arithmetic progression if $ a_1 = 101 ~~ \text{and} ~~ d = 1 $.	2
2971	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 0 $.	2
2972	Find $ a_{ 38 } $ of an arithmetic progression if $ a_1 = 2000 ~~ \text{and} ~~ d = 200 $.	2
2973	Find $ a_{ 59 } $ of an arithmetic progression if $ a_1 = 26 ~~ \text{and} ~~ d = 8 $.	2
2974	$$ a_1 = 7 ~~,~~ d = -4 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
2975	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 0 $.	2
2976	Find $ S_{ 500 } $ ( sum of first $ 500 $ terms ) of arithmetic progression if $ a_1 = 1050 ~~ \text{and} ~~ d = 50 $.	2
2977	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = 4 $.	2
2978	Find $ a_{ 65 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 9 $.	2
2979	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 7 $.	2
2980	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 3 $.	2
2981	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
2982	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -10 \right) $.	2
2983	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 22 ~~ \text{and} ~~ d = 1 $.	2
2984	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
2985	$$ a_1 = 2 ~~,~~ d = -3 ~~,~~ a_1 = ? ~~,~~ d = ? $$	2
2986	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 0 $.	2
2987	Find $ a_{ 68 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 7 $.	2
2988	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 6 $.	2
2989	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = \left( -11 \right) $.	2
2990	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = -23 ~~ \text{and} ~~ d = 5 $.	2
2991	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -3 \right) $.	2
2992	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 7 $.	2
2993	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
2994	Find $ a_{ 62 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $.	2
2995	Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 2 $.	2
2996	Find common difference $ d $ of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ a_{ 20 } = 72 $.	2
2997	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 38 $.	2
2998	Find $ a_{ 86 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 21 $.	2
2999	Find $ a_{ 86 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 3 $.	2
3000	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 0 $.	2