Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 8001 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 52 $. | 1 |
| 8002 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 9 ~~ \text{and} ~~ a_{ 14 } = 15 $. | 1 |
| 8003 | Find common difference $ d $ of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ a_{ 10 } = 43 $. | 1 |
| 8004 | Find common difference $ d $ of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ a_{ 21 } = 2 $. | 1 |
| 8005 | $$ a_1 = 10 ~,~ d = -\frac{ 2 }{ 5 } ~,~ a_n = 14 ~,~ n = ? $$ | 1 |
| 8006 | Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = 5 $. | 1 |
| 8007 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 1 $. | 1 |
| 8008 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 6 $. | 1 |
| 8009 | Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 3000 ~~ \text{and} ~~ d = \left( -250 \right) $. | 1 |
| 8010 | Find $ a_{ 48 } $ of an arithmetic progression if $ a_1 = 3000 ~~ \text{and} ~~ d = \left( -250 \right) $. | 1 |
| 8011 | Find $ a_{ 36 } $ of an arithmetic progression if $ a_1 = 5000 ~~ \text{and} ~~ d = 450 $. | 1 |
| 8012 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 4500 ~~ \text{and} ~~ d = 175 $. | 1 |
| 8013 | Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 4500 ~~ \text{and} ~~ d = 175 $. | 1 |
| 8014 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 1.004 ~~ \text{and} ~~ d = \left( -558 \right) $. | 1 |
| 8015 | Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 2 $. | 1 |
| 8016 | Find $ S_{ 200 } $ ( sum of first $ 200 $ terms ) of arithmetic progression if $ a_1 = 1015 ~~ \text{and} ~~ d = 5 $. | 1 |
| 8017 | Find $ a_{ 88 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 6 $. | 1 |
| 8018 | $$ a_1 = 13 ~,~ d = 6 ~,~ S_n = 88 ~,~ n = ? $$ | 1 |
| 8019 | Find $ S_{ 900 } $ ( sum of first $ 900 $ terms ) of arithmetic progression if $ a_1 = 101 ~~ \text{and} ~~ d = 1 $. | 1 |
| 8020 | Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 2 $. | 1 |
| 8021 | Find $ S_{ 58 } $ ( sum of first $ 58 $ terms ) of arithmetic progression if $ a_1 = 27 ~~ \text{and} ~~ d = 3 $. | 1 |
| 8022 | Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = \frac{ 7 }{ 2 } $. | 1 |
| 8023 | $$ a_1 = 1 ~,~ d = 5 ~,~ a_n = 6 ~,~ n = ? $$ | 1 |
| 8024 | Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 200 $. | 1 |
| 8025 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 3 $. | 1 |
| 8026 | $$ a_1 = 3 ~,~ d = 6 ~,~ a_n = 67 ~,~ n = ? $$ | 1 |
| 8027 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 7 $. | 1 |
| 8028 | Find $ a_{ 72 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = \left( -5 \right) $. | 1 |
| 8029 | Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 40 ~~ \text{and} ~~ d = -3 $. | 1 |
| 8030 | $$ a_1 = 6 ~,~ a_n = 20 ~,~ S_n = 625 ~,~ n = ? $$ | 1 |
| 8031 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 23 ~~ \text{and} ~~ d = 6 $. | 1 |
| 8032 | Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 222 ~~ \text{and} ~~ d = \left( -5 \right) $. | 1 |
| 8033 | Find $ a_{ 101 } $ of an arithmetic progression if $ a_1 = 222 ~~ \text{and} ~~ d = \left( -5 \right) $. | 1 |
| 8034 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 4 $. | 1 |
| 8035 | Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 0 $. | 1 |
| 8036 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $. | 1 |
| 8037 | Find $ a_{ 39 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $. | 1 |
| 8038 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = 0 $. | 1 |
| 8039 | Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $. | 1 |
| 8040 | Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $. | 1 |
| 8041 | Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = -225 ~~ \text{and} ~~ d = 78 $. | 1 |
| 8042 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 14 $. | 1 |
| 8043 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $. | 1 |
| 8044 | Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = \left( -7 \right) $. | 1 |
| 8045 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = -17 ~~ \text{and} ~~ d = -7 $. | 1 |
| 8046 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = \left( -4 \right) $. | 1 |
| 8047 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = \left( -2 \right) $. | 1 |
| 8048 | Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = -111 ~~ \text{and} ~~ d = 9 $. | 1 |
| 8049 | Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = -5 $. | 1 |
| 8050 | Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 10 $. | 1 |
