Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 6151 | Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $. | 1 |
| 6152 | Find $ S_{ 52 } $ ( sum of first $ 52 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $. | 1 |
| 6153 | Find $ S_{ 122 } $ ( sum of first $ 122 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 1 |
| 6154 | $$ a_1 = 5 ~,~ a_n = 45 ~,~ S_n = 120 ~,~ n = ? $$ | 1 |
| 6155 | Find $ a_{ 300 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 1 |
| 6156 | Find $ S_{ 300 } $ ( sum of first $ 300 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 1 |
| 6157 | Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 336 ~~ \text{and} ~~ d = 1 $. | 1 |
| 6158 | Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 4 $. | 1 |
| 6159 | Find common difference $ d $ of arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ a_{ 26 } = 165 $. | 1 |
| 6160 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -3 \right) $. | 1 |
| 6161 | Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 10 $. | 1 |
| 6162 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = 5 $. | 1 |
| 6163 | Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 27 ~~ \text{and} ~~ d = 7 $. | 1 |
| 6164 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $. | 1 |
| 6165 | Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 4 $. | 1 |
| 6166 | Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 4 $. | 1 |
| 6167 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = \left( -\frac{ 6 }{ 5 } \right) $. | 1 |
| 6168 | Find $ a_{ 36 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = \left( -\frac{ 6 }{ 5 } \right) $. | 1 |
| 6169 | Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = \frac{ 4 }{ 9 } ~~ \text{and} ~~ d = \frac{ 2 }{ 9 } $. | 1 |
| 6170 | Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = -6 $. | 1 |
| 6171 | Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = -6 $. | 1 |
| 6172 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = \left( -2 \right) $. | 1 |
| 6173 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = \left( -3 \right) $. | 1 |
| 6174 | Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = \left( -3 \right) $. | 1 |
| 6175 | Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = -3 $. | 1 |
| 6176 | Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 7 $. | 1 |
| 6177 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 7 $. | 1 |
| 6178 | Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 20 } \right) $. | 1 |
| 6179 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $. | 1 |
| 6180 | Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = -2 $. | 1 |
| 6181 | Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 6 $. | 1 |
| 6182 | Find $ a_{ 42 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 2 $. | 1 |
| 6183 | Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $. | 1 |
| 6184 | Find $ a_{ 85 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 13 $. | 1 |
| 6185 | Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 9 $. | 1 |
| 6186 | Find $ a_{ 96 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -5 \right) $. | 1 |
| 6187 | Find $ a_{ 75 } $ of an arithmetic progression if $ a_1 = -17 ~~ \text{and} ~~ d = \left( -4 \right) $. | 1 |
| 6188 | Find $ a_{ 73 } $ of an arithmetic progression if $ a_1 = -28 ~~ \text{and} ~~ d = \left( -27 \right) $. | 1 |
| 6189 | Find $ a_{ 73 } $ of an arithmetic progression if $ a_1 = -28 ~~ \text{and} ~~ d = \left( -13 \right) $. | 1 |
| 6190 | Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = -13 ~~ \text{and} ~~ d = -11 $. | 1 |
| 6191 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \left( -5 \right) $. | 1 |
| 6192 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 11 $. | 1 |
| 6193 | $$ a_1 = 20 ~,~ d = 4 ~,~ a_n = 144 ~,~ n = ? $$ | 1 |
| 6194 | $$ a_1 = 20 ~,~ d = 4 ~,~ S_n = 144 ~,~ n = ? $$ | 1 |
| 6195 | Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = -\frac{ 1 }{ 3 } $. | 1 |
| 6196 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 1 |
| 6197 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 1 $. | 1 |
| 6198 | $$ a_1 = 11 ~,~ d = -\frac{ 1 }{ 5 } ~,~ a_n = -\frac{ 6 }{ 5 } ~,~ n = ? $$ | 1 |
| 6199 | Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 4 $. | 1 |
| 6200 | Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 9 $. | 1 |
