Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 1 | Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 20 |
| 2 | Find $ S_{ 365 } $ ( sum of first $ 365 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 19 |
| 3 | Find $ a_1 $ (first term of arithmetic progression) if $ d = \frac{ 4 }{ 3 } ~~ \text{and} ~~ a_{ 8 } = 5 $. | 16 |
| 4 | $$ a_1 = -6 ~,~ d = 2 ~,~ S_n = -10 ~,~ n = ? $$ | 13 |
| 5 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 12 |
| 6 | Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 0 $. | 12 |
| 7 | Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 7 $. | 11 |
| 8 | Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 11 |
| 9 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 100 } ~~ \text{and} ~~ d = \frac{ 1 }{ 100 } $. | 10 |
| 10 | $$ a_1 = -12 ~,~ d = 3 ~,~ S_n = 1104 ~,~ n = ? $$ | 9 |
| 11 | $$ a_{ 12 } = 15 ~~,~~ S_{ 9 } = 55 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 9 |
| 12 | Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 6 $. | 9 |
| 13 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 0 $. | 9 |
| 14 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 0 $. | 9 |
| 15 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 12 $. | 8 |
| 16 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $. | 8 |
| 17 | Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 58 ~~ \text{and} ~~ d = 23 $. | 8 |
| 18 | Find $ a_{ 41 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 0 $. | 8 |
| 19 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $. | 8 |
| 20 | Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 8 |
| 21 | Find $ S_{ 89 } $ ( sum of first $ 89 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 7 |
| 22 | Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 2 $. | 7 |
| 23 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $. | 7 |
| 24 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = -4 $. | 7 |
| 25 | Find $ S_{ 45 } $ ( sum of first $ 45 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $. | 6 |
| 26 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 2 $. | 6 |
| 27 | Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 96 ~~ \text{and} ~~ d = 94 $. | 6 |
| 28 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -4 \right) $. | 6 |
| 29 | Find $ a_{ 41 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -6 \right) $. | 6 |
| 30 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 5 } ~~ \text{and} ~~ d = \frac{ 7 }{ 5 } $. | 6 |
| 31 | Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 185 ~~ \text{and} ~~ d = 5 $. | 6 |
| 32 | Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 8 $. | 6 |
| 33 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $. | 6 |
| 34 | Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $. | 6 |
| 35 | Find $ a_{ 37 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = \frac{ 14 }{ 5 } $. | 6 |
| 36 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 20 $. | 6 |
| 37 | Find $ a_{ 365 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 6 |
| 38 | Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 7 $. | 6 |
| 39 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 3 $. | 6 |
| 40 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 27 ~~ \text{and} ~~ d = \left( -5 \right) $. | 6 |
| 41 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $. | 6 |
| 42 | $$ a_1 = 30 ~,~ d = 10 ~,~ S_n = 1500 ~,~ n = ? $$ | 6 |
| 43 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $. | 6 |
| 44 | Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 10 $. | 6 |
| 45 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 47 }{ 160 } $. | 6 |
| 46 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = \left( -3 \right) $. | 5 |
| 47 | Find $ S_{ 121 } $ ( sum of first $ 121 $ terms ) of arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = -4 $. | 5 |
| 48 | Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = -3 $. | 5 |
| 49 | Find $ S_{ 52 } $ ( sum of first $ 52 $ terms ) of arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 3 $. | 5 |
| 50 | $$ a_1 = 1491 ~,~ d = -7 ~,~ S_n = 0 ~,~ n = ? $$ | 5 |
