Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 10201 | $$ a_{ 5 } = 15 ~~,~~ S_{ 8 } = 27 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 10202 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 4 ~~ \text{and} ~~ a_{ 5 } = 15 $. | 1 |
| 10203 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 9 ~~ \text{and} ~~ a_{ 5 } = 53 $. | 1 |
| 10204 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 10 ~~ \text{and} ~~ a_{ 20 } = 191 $. | 1 |
| 10205 | $$ d = 2 ~,~ a_n = 17 ~,~ S_n = 42 ~,~ n = ? $$ | 1 |
| 10206 | Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 8 $. | 1 |
| 10207 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = 7 $. | 1 |
| 10208 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $. | 1 |
| 10209 | Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 1 $. | 1 |
| 10210 | $$ a_1 = 2 ~,~ d = 2 ~,~ a_n = 464 ~,~ n = ? $$ | 1 |
| 10211 | Find $ S_{ 232 } $ ( sum of first $ 232 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $. | 1 |
| 10212 | Find $ a_{ 55 } $ of an arithmetic progression if $ a_1 = 89 ~~ \text{and} ~~ d = 16 $. | 1 |
| 10213 | $$ a_{ 19 } = 57 ~~,~~ S_{ 36 } = 2034 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 10214 | Find $ S_{ 126 } $ ( sum of first $ 126 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = -4 $. | 1 |
| 10215 | Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = \left( -5 \right) $. | 1 |
| 10216 | Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 8 $. | 1 |
| 10217 | Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 105 ~~ \text{and} ~~ d = \left( -5 \right) $. | 1 |
| 10218 | Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 105 ~~ \text{and} ~~ d = \left( -5 \right) $. | 1 |
| 10219 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 8 $. | 1 |
| 10220 | $$ a_1 = \frac{ 55 }{ 2 } ~,~ d = \frac{ 5 }{ 2 } ~,~ S_n = 1400 ~,~ n = ? $$ | 1 |
| 10221 | Find $ a_{ 1438 } $ of an arithmetic progression if $ a_1 = 38 ~~ \text{and} ~~ d = 200 $. | 1 |
| 10222 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -23 ~~ \text{and} ~~ d = 5 $. | 1 |
| 10223 | Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $. | 1 |
| 10224 | Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 20 $. | 1 |
| 10225 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = 4 $. | 1 |
| 10226 | Find $ a_{ 38 } $ of an arithmetic progression if $ a_1 = -\frac{ 266 }{ 5 } ~~ \text{and} ~~ d = \left( -\frac{ 11 }{ 10 } \right) $. | 1 |
| 10227 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $. | 1 |
| 10228 | Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 7 $. | 1 |
| 10229 | Find $ a_{ 61 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 5 $. | 1 |
| 10230 | Find $ a_1 $ (first term of arithmetic progression) if $ d = -7 ~~ \text{and} ~~ a_{ 7 } = -8 $. | 1 |
| 10231 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 3 $. | 1 |
| 10232 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -14 ~~ \text{and} ~~ d = 3 $. | 1 |
| 10233 | Find $ S_{ 41 } $ ( sum of first $ 41 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = -5 $. | 1 |
| 10234 | Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 500 $. | 1 |
| 10235 | Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 500 $. | 1 |
| 10236 | Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 8 $. | 1 |
| 10237 | Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 12 $. | 1 |
| 10238 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 6 $. | 1 |
| 10239 | Find $ S_{ 250 } $ ( sum of first $ 250 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $. | 1 |
| 10240 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 2 $. | 1 |
| 10241 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 0 $. | 1 |
| 10242 | Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $. | 1 |
| 10243 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 56 ~~ \text{and} ~~ d = \left( -4 \right) $. | 1 |
| 10244 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 5 } ~~ \text{and} ~~ d = \frac{ 1 }{ 5 } $. | 1 |
| 10245 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 2 $. | 1 |
| 10246 | Find $ S_{ 140 } $ ( sum of first $ 140 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $. | 1 |
| 10247 | $$ a_1 = -11 ~~,~~ d = 7 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 10248 | Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 1 |
| 10249 | Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 1 |
| 10250 | Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 1 |
