Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 8201 | Find $ a_1 $ (first term of arithmetic progression) if $ d = -11 ~~ \text{and} ~~ a_{ 15 } = 15 $. | 1 |
| 8202 | Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = \left( -1 \right) $. | 1 |
| 8203 | Find $ a_{ 38 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 3 $. | 1 |
| 8204 | Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = \left( -10 \right) $. | 1 |
| 8205 | Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = -13 ~~ \text{and} ~~ d = 7 $. | 1 |
| 8206 | Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = -6 $. | 1 |
| 8207 | Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 7 $. | 1 |
| 8208 | Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 9 $. | 1 |
| 8209 | Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 22 ~~ \text{and} ~~ d = \left( -8 \right) $. | 1 |
| 8210 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = \left( -2 \right) $. | 1 |
| 8211 | Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $. | 1 |
| 8212 | Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = 4 $. | 1 |
| 8213 | Find $ a_{ 27 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $. | 1 |
| 8214 | Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -6 \right) $. | 1 |
| 8215 | Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -1 \right) $. | 1 |
| 8216 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = \left( -34 \right) $. | 1 |
| 8217 | Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = 48 ~~ \text{and} ~~ d = 0 $. | 1 |
| 8218 | Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = \left( -5 \right) $. | 1 |
| 8219 | Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = 48 ~~ \text{and} ~~ d = 1 $. | 1 |
| 8220 | Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 48 ~~ \text{and} ~~ d = 1 $. | 1 |
| 8221 | $$ a_1 = 48 ~~,~~ d = 0 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 8222 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 0 ~~ \text{and} ~~ S_{ 33 } = 1536 $. | 1 |
| 8223 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 0 $. | 1 |
| 8224 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 7 $. | 1 |
| 8225 | Find $ a_{ 309 } $ of an arithmetic progression if $ a_1 = 33 ~~ \text{and} ~~ d = 3 $. | 1 |
| 8226 | Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = -4 $. | 1 |
| 8227 | Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 42 ~~ \text{and} ~~ d = -3 $. | 1 |
| 8228 | Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 38 ~~ \text{and} ~~ d = -3 $. | 1 |
| 8229 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 38 ~~ \text{and} ~~ d = -3 $. | 1 |
| 8230 | Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 38 ~~ \text{and} ~~ d = -3 $. | 1 |
| 8231 | Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 39 ~~ \text{and} ~~ d = -3 $. | 1 |
| 8232 | Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 39 ~~ \text{and} ~~ d = -3 $. | 1 |
| 8233 | $$ a_1 = 2 ~~,~~ d = 2 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 8234 | $$ a_1 = 2 ~~,~~ d = 2 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 8235 | $$ a_1 = 2 ~~,~~ d = 2 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 8236 | $$ a_1 = 2 ~~,~~ d = 2 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 8237 | Find $ S_{ 17 } $ ( sum of first $ 17 $ terms ) of arithmetic progression if $ a_1 = 39 ~~ \text{and} ~~ d = -3 $. | 1 |
| 8238 | $$ a_1 = 2 ~,~ d = 2 ~,~ S_n = 52 ~,~ n = ? $$ | 1 |
| 8239 | $$ a_1 = 1 ~,~ d = 2 ~,~ a_n = 52 ~,~ n = ? $$ | 1 |
| 8240 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 1 $. | 1 |
| 8241 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 26 $. | 1 |
| 8242 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = \frac{ 9 }{ 2 } ~~ \text{and} ~~ d = -\frac{ 7 }{ 2 } $. | 1 |
| 8243 | Find $ d $ (common difference of arithmetic progression) if $ a_1 = 5 ~~ \text{and} ~~ S_{ 5 } = 18 $. | 1 |
| 8244 | Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $. | 1 |
| 8245 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 14 $. | 1 |
| 8246 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 14 $. | 1 |
| 8247 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 3600000 ~~ \text{and} ~~ d = 200000 $. | 1 |
| 8248 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 200000 ~~ \text{and} ~~ S_{ 5 } = 45000000 $. | 1 |
| 8249 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 200000 ~~ \text{and} ~~ S_{ 10 } = 45000000 $. | 1 |
| 8250 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 1000000 ~~ \text{and} ~~ S_{ 10 } = 45000000 $. | 1 |
