Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 6201 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 2 ~~ \text{and} ~~ a_{ 15 } = 11 $. | 1 |
| 6202 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = -17 ~~ \text{and} ~~ d = 2 $. | 1 |
| 6203 | Find $ S_{ 27 } $ ( sum of first $ 27 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 1 $. | 1 |
| 6204 | Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 15 $. | 1 |
| 6205 | Find $ S_{ 1050 } $ ( sum of first $ 1050 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 1 |
| 6206 | Find $ a_{ 1240 } $ of an arithmetic progression if $ a_1 = 751 ~~ \text{and} ~~ d = 1 $. | 1 |
| 6207 | Find $ S_{ 751 } $ ( sum of first $ 751 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 1 |
| 6208 | Find $ S_{ 1240 } $ ( sum of first $ 1240 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 1 |
| 6209 | Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $. | 1 |
| 6210 | Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $. | 1 |
| 6211 | $$ a_1 = \frac{ 11 }{ 8 } ~,~ d = \frac{ 1 }{ 2 } ~,~ a_n = 23 ~,~ n = ? $$ | 1 |
| 6212 | Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $. | 1 |
| 6213 | $$ a_1 = 3 ~,~ d = 5 ~,~ a_n = 288 ~,~ n = ? $$ | 1 |
| 6214 | Find $ a_{ 41 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $. | 1 |
| 6215 | Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $. | 1 |
| 6216 | Find $ S_{ 39 } $ ( sum of first $ 39 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = -\frac{ 1 }{ 2 } $. | 1 |
| 6217 | $$ a_1 = -8 ~~,~~ d = 7 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 6218 | Find $ a_{ 135 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $. | 1 |
| 6219 | $$ a_{ 20 } = 80 ~~,~~ S_{ 50 } = -100 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 6220 | $$ a_{ 3 } = 8 ~~,~~ S_{ 6 } = 0.512 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 6221 | $$ a_1 = 11 ~~,~~ d = -6 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 6222 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = \left( -6 \right) $. | 1 |
| 6223 | Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 56 ~~ \text{and} ~~ d = -7 $. | 1 |
| 6224 | Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $. | 1 |
| 6225 | Find $ S_{ 36 } $ ( sum of first $ 36 $ terms ) of arithmetic progression if $ a_1 = 255 ~~ \text{and} ~~ d = 5 $. | 1 |
| 6226 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = \left( -7 \right) $. | 1 |
| 6227 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = \left( -7 \right) $. | 1 |
| 6228 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = -7 $. | 1 |
| 6229 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 0 $. | 1 |
| 6230 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = \frac{ 4 }{ 3 } ~~ \text{and} ~~ d = \frac{ 11 }{ 7 } $. | 1 |
| 6231 | Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \left( -8 \right) $. | 1 |
| 6232 | Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = -\frac{ 15 }{ 2 } ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $. | 1 |
| 6233 | Find $ a_{ 470 } $ of an arithmetic progression if $ a_1 = 300 ~~ \text{and} ~~ d = 10 $. | 1 |
| 6234 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 34 ~~ \text{and} ~~ d = 1 $. | 1 |
| 6235 | Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $. | 1 |
| 6236 | Find $ a_{ 64 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 1 $. | 1 |
| 6237 | Find $ a_{ 68 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 1 $. | 1 |
| 6238 | Find $ S_{ 81 } $ ( sum of first $ 81 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 6 $. | 1 |
| 6239 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = \left( -7 \right) $. | 1 |
| 6240 | Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 50 $. | 1 |
| 6241 | Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 2 $. | 1 |
| 6242 | Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 2 $. | 1 |
| 6243 | Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 3 $. | 1 |
| 6244 | Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 4 $. | 1 |
| 6245 | Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 5 $. | 1 |
| 6246 | Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 7 $. | 1 |
| 6247 | $$ a_1 = 5 ~~,~~ d = -7 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 6248 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 1220 ~~ \text{and} ~~ d = 60 $. | 1 |
| 6249 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 1220 ~~ \text{and} ~~ d = 60 $. | 1 |
| 6250 | Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = -\frac{ 1 }{ 100 } $. | 1 |
