Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 10051 | Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 13 }{ 10 } $. | 1 |
| 10052 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 5 $. | 1 |
| 10053 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 15 $. | 1 |
| 10054 | Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 14 $. | 1 |
| 10055 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 20 $. | 1 |
| 10056 | Find $ S_{ 3 } $ ( sum of first $ 3 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $. | 1 |
| 10057 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 200 $. | 1 |
| 10058 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 200 $. | 1 |
| 10059 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = \left( -4 \right) $. | 1 |
| 10060 | Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = \left( -4 \right) $. | 1 |
| 10061 | Find $ a_{ 65 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 3 $. | 1 |
| 10062 | Find $ a_{ 65 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 5 $. | 1 |
| 10063 | Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 9 $. | 1 |
| 10064 | Find $ a_{ 63 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $. | 1 |
| 10065 | Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 6 $. | 1 |
| 10066 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 1 $. | 1 |
| 10067 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 7 $. | 1 |
| 10068 | Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 7 $. | 1 |
| 10069 | Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 45 ~~ \text{and} ~~ d = 2 $. | 1 |
| 10070 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 15 $. | 1 |
| 10071 | Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 22 $. | 1 |
| 10072 | $$ a_1 = 50 ~,~ d = 20 ~,~ a_n = 3200 ~,~ n = ? $$ | 1 |
| 10073 | $$ a_{ 11 } = 1164 ~~,~~ S_{ 33 } = 3672 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 10074 | Find $ a_{ 166 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $. | 1 |
| 10075 | Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $. | 1 |
| 10076 | Find $ S_{ 148 } $ ( sum of first $ 148 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $. | 1 |
| 10077 | $$ a_1 = 14 ~,~ a_n = -85 ~,~ S_n = -1207 ~,~ n = ? $$ | 1 |
| 10078 | Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \frac{ 51 }{ 10 } $. | 1 |
| 10079 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -\frac{ 26 }{ 5 } \right) $. | 1 |
| 10080 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -\frac{ 53 }{ 10 } \right) $. | 1 |
| 10081 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -\frac{ 11 }{ 2 } \right) $. | 1 |
| 10082 | Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = -\frac{ 11 }{ 2 } $. | 1 |
| 10083 | Find $ S_{ 1 } $ ( sum of first $ 1 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = -\frac{ 11 }{ 2 } $. | 1 |
| 10084 | Find $ a_{ 93 } $ of an arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = \left( -4 \right) $. | 1 |
| 10085 | Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = -4 $. | 1 |
| 10086 | Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 51 }{ 10 } $. | 1 |
| 10087 | Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 26 }{ 5 } $. | 1 |
| 10088 | Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 11 }{ 2 } $. | 1 |
| 10089 | Find $ a_1 $ (first term of arithmetic progression) if $ d = -3 ~~ \text{and} ~~ a_{ 15 } = 28 $. | 1 |
| 10090 | Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 7 $. | 1 |
| 10091 | Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = 2 $. | 1 |
| 10092 | Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = 4 $. | 1 |
| 10093 | Find $ a_{ 45 } $ of an arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = 4 $. | 1 |
| 10094 | $$ a_1 = 5 ~,~ d = 2 ~,~ a_n = 1310720 ~,~ n = ? $$ | 1 |
| 10095 | Find common difference $ d $ of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ a_{ 29 } = 20 $. | 1 |
| 10096 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 1 |
| 10097 | Find $ a_{ 432 } $ of an arithmetic progression if $ a_1 = 78 ~~ \text{and} ~~ d = 9 $. | 1 |
| 10098 | Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $. | 1 |
| 10099 | Find $ S_{ 79 } $ ( sum of first $ 79 $ terms ) of arithmetic progression if $ a_1 = 79 ~~ \text{and} ~~ d = -1 $. | 1 |
| 10100 | Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = -7 $. | 1 |
