Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 9101 | $$ a_1 = 80 ~,~ a_n = 5 ~,~ S_n = 240 ~,~ n = ? $$ | 1 |
| 9102 | Find $ d $ (common difference of arithmetic progression) if $ a_1 = 80 ~~ \text{and} ~~ S_{ 5 } = 240 $. | 1 |
| 9103 | $$ a_1 = 7 ~,~ d = -2 ~,~ S_n = -2900 ~,~ n = ? $$ | 1 |
| 9104 | Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 81 ~~ \text{and} ~~ d = 0 $. | 1 |
| 9105 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = \frac{ 5 }{ 2 } ~~ \text{and} ~~ d = 3 $. | 1 |
| 9106 | Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \left( -3 \right) $. | 1 |
| 9107 | Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = \left( -3 \right) $. | 1 |
| 9108 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $. | 1 |
| 9109 | Find $ a_{ 48 } $ of an arithmetic progression if $ a_1 = 2400 ~~ \text{and} ~~ d = 0.011 $. | 1 |
| 9110 | Find $ a_{ 48 } $ of an arithmetic progression if $ a_1 = 2400 ~~ \text{and} ~~ d = 1.011 $. | 1 |
| 9111 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 2400 ~~ \text{and} ~~ d = 24 $. | 1 |
| 9112 | Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 15 $. | 1 |
| 9113 | Find $ a_{ 36 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 25 $. | 1 |
| 9114 | Find $ S_{ 35 } $ ( sum of first $ 35 $ terms ) of arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 25 $. | 1 |
| 9115 | Find $ a_{ 200000 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 1 |
| 9116 | Find $ S_{ 200000 } $ ( sum of first $ 200000 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 1 |
| 9117 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 3 } \right) $. | 1 |
| 9118 | Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = \frac{ 2 }{ 5 } ~~ \text{and} ~~ d = 5 $. | 1 |
| 9119 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 92 ~~ \text{and} ~~ d = \left( -4 \right) $. | 1 |
| 9120 | Find $ S_{ 60 } $ ( sum of first $ 60 $ terms ) of arithmetic progression if $ a_1 = 31 ~~ \text{and} ~~ d = 1 $. | 1 |
| 9121 | Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 8 $. | 1 |
| 9122 | Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 2 $. | 1 |
| 9123 | Find $ S_{ 22 } $ ( sum of first $ 22 $ terms ) of arithmetic progression if $ a_1 = 63700 ~~ \text{and} ~~ d = 1500 $. | 1 |
| 9124 | Find $ S_{ 22 } $ ( sum of first $ 22 $ terms ) of arithmetic progression if $ a_1 = 63700 ~~ \text{and} ~~ d = 2000 $. | 1 |
| 9125 | Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 63700 ~~ \text{and} ~~ d = 2000 $. | 1 |
| 9126 | $$ a_1 = 1 ~,~ d = 1 ~,~ S_n = 5019 ~,~ n = ? $$ | 1 |
| 9127 | $$ a_1 = 1 ~,~ d = 1 ~,~ a_n = 5019 ~,~ n = ? $$ | 1 |
| 9128 | Find $ S_{ 5019 } $ ( sum of first $ 5019 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 1 |
| 9129 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \frac{ 3 }{ 10 } $. | 1 |
| 9130 | Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $. | 1 |
| 9131 | Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 2000 ~~ \text{and} ~~ d = 200 $. | 1 |
| 9132 | Find $ a_{ 65536 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $. | 1 |
| 9133 | $$ a_{ 2 } = 15 ~~,~~ S_{ 3 } = 105 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 9134 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = \left( -10 \right) $. | 1 |
| 9135 | Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \left( -2 \right) $. | 1 |
| 9136 | Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \left( -2 \right) $. | 1 |
| 9137 | Find $ S_{ 49 } $ ( sum of first $ 49 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 1 $. | 1 |
| 9138 | Find $ a_{ 60000 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 0 $. | 1 |
| 9139 | Find $ S_{ 60000 } $ ( sum of first $ 60000 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 0 $. | 1 |
| 9140 | Find $ S_{ 60000 } $ ( sum of first $ 60000 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 0 $. | 1 |
| 9141 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 15 $. | 1 |
| 9142 | Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $. | 1 |
| 9143 | Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = -3 $. | 1 |
| 9144 | Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = -3 $. | 1 |
| 9145 | Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = \left( -4 \right) $. | 1 |
| 9146 | Find $ S_{ 102 } $ ( sum of first $ 102 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $. | 1 |
| 9147 | Find $ a_{ 649 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $. | 1 |
| 9148 | Find $ S_{ 41 } $ ( sum of first $ 41 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 8 $. | 1 |
| 9149 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 10 $. | 1 |
| 9150 | Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 10 $. | 1 |
