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
2601	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 3 $.	3
2602	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = \left( -4 \right) $.	3
2603	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = -8 $.	3
2604	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 8 $.	3
2605	Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = \left( -7 \right) $.	3
2606	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 10 $.	3
2607	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = -3 $.	3
2608	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $.	3
2609	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	3
2610	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	3
2611	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 4 $.	3
2612	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 8 $.	3
2613	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -\frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $.	3
2614	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $.	3
2615	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 45 ~~ \text{and} ~~ d = \left( -\frac{ 3 }{ 2 } \right) $.	3
2616	Find $ a_{ 72 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -3 \right) $.	3
2617	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 7 $.	3
2618	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 6 $.	3
2619	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \frac{ 2 }{ 3 } $.	3
2620	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 894 ~~ \text{and} ~~ d = \left( -7 \right) $.	3
2621	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 39 ~~ \text{and} ~~ d = \left( -5 \right) $.	3
2622	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -\frac{ 46 }{ 5 } ~~ \text{and} ~~ d = \frac{ 9 }{ 10 } $.	3
2623	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \left( -9 \right) $.	3
2624	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 10 $.	3
2625	Find $ a_{ 48 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $.	3
2626	Find $ S_{ 301 } $ ( sum of first $ 301 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	3
2627	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $.	3
2628	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \frac{ 27 }{ 5 } $.	3
2629	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = -7 $.	3
2630	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $.	3
2631	Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = 7 $.	3
2632	Find $ a_{ 39 } $ of an arithmetic progression if $ a_1 = 65 ~~ \text{and} ~~ d = 100 $.	3
2633	Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 0 $.	3
2634	Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = -1 $.	3
2635	Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = -1 $.	3
2636	Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = -\frac{ 71 }{ 10 } ~~ \text{and} ~~ d = \frac{ 21 }{ 10 } $.	3
2637	Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 8 $.	3
2638	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 8 $.	3
2639	Find $ a_{ 64 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 6 $.	3
2640	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 7 $.	3
2641	Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = -\frac{ 1 }{ 5 } $.	3
2642	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = -\frac{ 1 }{ 5 } $.	3
2643	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = -\frac{ 1 }{ 5 } $.	3
2644	Find $ S_{ 90 } $ ( sum of first $ 90 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	3
2645	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 4 $.	3
2646	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	3
2647	Find $ S_{ 57 } $ ( sum of first $ 57 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $.	3
2648	Find $ a_{ 57 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $.	3
2649	Find $ S_{ 91 } $ ( sum of first $ 91 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 1 $.	3
2650	Find $ S_{ 37 } $ ( sum of first $ 37 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = -7 $.	3