Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 10001 | Find $ S_{ 4460 } $ ( sum of first $ 4460 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 100 $. | 1 |
| 10002 | Find $ S_{ 4465 } $ ( sum of first $ 4465 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 100 $. | 1 |
| 10003 | Find $ S_{ 4461 } $ ( sum of first $ 4461 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 100 $. | 1 |
| 10004 | Find $ S_{ 4462 } $ ( sum of first $ 4462 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 100 $. | 1 |
| 10005 | Find $ a_{ 4463 } $ of an arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 100 $. | 1 |
| 10006 | Find $ a_{ 255 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 25 $. | 1 |
| 10007 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 6 $. | 1 |
| 10008 | Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = -13 ~~ \text{and} ~~ d = 6 $. | 1 |
| 10009 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 2 $. | 1 |
| 10010 | Find $ S_{ 60 } $ ( sum of first $ 60 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $. | 1 |
| 10011 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 28000 ~~ \text{and} ~~ d = 2800 $. | 1 |
| 10012 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 37000 ~~ \text{and} ~~ d = 700 $. | 1 |
| 10013 | $$ a_1 = 25 ~,~ d = 8 ~,~ a_n = 145 ~,~ n = ? $$ | 1 |
| 10014 | $$ a_1 = 8 ~,~ d = 3 ~,~ a_n = 338 ~,~ n = ? $$ | 1 |
| 10015 | Find $ a_{ 49 } $ of an arithmetic progression if $ a_1 = 70 ~~ \text{and} ~~ d = \left( -7 \right) $. | 1 |
| 10016 | $$ a_1 = 100 ~,~ d = 3 ~,~ a_n = 1000 ~,~ n = ? $$ | 1 |
| 10017 | Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = 21000 ~~ \text{and} ~~ d = 6 $. | 1 |
| 10018 | $$ a_1 = 20 ~,~ d = -4 ~,~ a_n = -140 ~,~ n = ? $$ | 1 |
| 10019 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 36000 $. | 1 |
| 10020 | Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 3 $. | 1 |
| 10021 | Find $ S_{ 500 } $ ( sum of first $ 500 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = \frac{ 2 }{ 5 } $. | 1 |
| 10022 | Find $ S_{ 44 } $ ( sum of first $ 44 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $. | 1 |
| 10023 | Find $ S_{ 45 } $ ( sum of first $ 45 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $. | 1 |
| 10024 | Find $ a_{ 47 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $. | 1 |
| 10025 | Find $ a_{ 85 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \frac{ 1 }{ 12 } $. | 1 |
| 10026 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = \frac{ 23 }{ 20 } ~~ \text{and} ~~ d = \frac{ 117 }{ 4 } $. | 1 |
| 10027 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -4 \right) $. | 1 |
| 10028 | Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 130 ~~ \text{and} ~~ d = 80 $. | 1 |
| 10029 | Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 4 $. | 1 |
| 10030 | Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = 35 $. | 1 |
| 10031 | $$ a_1 = 25 ~,~ d = 2 ~,~ a_n = 80 ~,~ n = ? $$ | 1 |
| 10032 | Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = -3 $. | 1 |
| 10033 | Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = -1 $. | 1 |
| 10034 | Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = -1 $. | 1 |
| 10035 | Find $ S_{ 29 } $ ( sum of first $ 29 $ terms ) of arithmetic progression if $ a_1 = \frac{ 7 }{ 10 } ~~ \text{and} ~~ d = 2 $. | 1 |
| 10036 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = \frac{ 13 }{ 4 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $. | 1 |
| 10037 | Find common difference $ d $ of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ a_{ 8 } = 35 $. | 1 |
| 10038 | $$ a_1 = 7 ~,~ d = 90 ~,~ a_n = 89 ~,~ n = ? $$ | 1 |
| 10039 | Find $ a_{ 978 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 89 $. | 1 |
| 10040 | Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 10 $. | 1 |
| 10041 | $$ a_1 = 2 ~,~ d = -6 ~,~ a_n = 21 ~,~ n = ? $$ | 1 |
| 10042 | Find $ S_{ 125 } $ ( sum of first $ 125 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $. | 1 |
| 10043 | Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 1105 ~~ \text{and} ~~ d = 20 $. | 1 |
| 10044 | Find $ d $ (common difference of arithmetic progression) if $ a_1 = 2 ~~ \text{and} ~~ S_{ 3 } = 36 $. | 1 |
| 10045 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 35 ~~ \text{and} ~~ d = \left( -3 \right) $. | 1 |
| 10046 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -7 ~~ \text{and} ~~ d = -2 $. | 1 |
| 10047 | $$ a_1 = 20 ~,~ d = -3 ~,~ S_n = 55 ~,~ n = ? $$ | 1 |
| 10048 | Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -4 \right) $. | 1 |
| 10049 | Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $. | 1 |
| 10050 | Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = \frac{ 1 }{ 3 } $. | 1 |
