Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 1001 | Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 12 $. | 5 |
| 1002 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \left( -3 \right) $. | 5 |
| 1003 | Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = \frac{ 17 }{ 5 } ~~ \text{and} ~~ d = \frac{ 33 }{ 10 } $. | 5 |
| 1004 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 2 $. | 5 |
| 1005 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 27 ~~ \text{and} ~~ d = 2 $. | 5 |
| 1006 | Find $ a_{ 68 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $. | 5 |
| 1007 | Find $ a_{ 79 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 2 $. | 5 |
| 1008 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 0 $. | 5 |
| 1009 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 4 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 8 } \right) $. | 5 |
| 1010 | Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 13 $. | 5 |
| 1011 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 0 $. | 5 |
| 1012 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 7 $. | 5 |
| 1013 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = \frac{ 3 }{ 4 } ~~ \text{and} ~~ d = \frac{ 1 }{ 8 } $. | 5 |
| 1014 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 4 } ~~ \text{and} ~~ d = 19 $. | 5 |
| 1015 | Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -3 \right) $. | 5 |
| 1016 | Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -3 \right) $. | 5 |
| 1017 | Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -3 \right) $. | 5 |
| 1018 | Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -3 \right) $. | 5 |
| 1019 | Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -3 \right) $. | 5 |
| 1020 | Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 10 $. | 5 |
| 1021 | $$ a_1 = 3 ~,~ d = 12 ~,~ S_n = 360 ~,~ n = ? $$ | 5 |
| 1022 | $$ a_1 = 3 ~,~ d = 2 ~,~ S_n = 360 ~,~ n = ? $$ | 5 |
| 1023 | Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 0 $. | 5 |
| 1024 | $$ a_1 = 20 ~~,~~ d = 3 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 5 |
| 1025 | Find $ a_{ 38 } $ of an arithmetic progression if $ a_1 = 18000 ~~ \text{and} ~~ d = 4000 $. | 5 |
| 1026 | Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 95 ~~ \text{and} ~~ d = 24 $. | 5 |
| 1027 | Find $ S_{ 289 } $ ( sum of first $ 289 $ terms ) of arithmetic progression if $ a_1 = 95 ~~ \text{and} ~~ d = 24 $. | 5 |
| 1028 | Find $ a_{ 93 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = 1 $. | 5 |
| 1029 | Find $ S_{ 75 } $ ( sum of first $ 75 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = -4 $. | 5 |
| 1030 | Find $ S_{ 41 } $ ( sum of first $ 41 $ terms ) of arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = 4 $. | 5 |
| 1031 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = -90 ~~ \text{and} ~~ d = -30 $. | 5 |
| 1032 | Find $ a_{ 55 } $ of an arithmetic progression if $ a_1 = \frac{ 17 }{ 5 } ~~ \text{and} ~~ d = \frac{ 17 }{ 10 } $. | 5 |
| 1033 | Find $ a_{ 56 } $ of an arithmetic progression if $ a_1 = \frac{ 17 }{ 5 } ~~ \text{and} ~~ d = \frac{ 17 }{ 10 } $. | 5 |
| 1034 | Find $ S_{ 70 } $ ( sum of first $ 70 $ terms ) of arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = -20 $. | 5 |
| 1035 | Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $. | 5 |
| 1036 | Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $. | 5 |
| 1037 | Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 5 $. | 5 |
| 1038 | Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 2 $. | 5 |
| 1039 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 10 $. | 5 |
| 1040 | Find $ a_{ 41 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 6 $. | 5 |
| 1041 | Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 5 |
| 1042 | Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 5 $. | 5 |
| 1043 | $$ a_1 = 14 ~,~ d = 11 ~,~ a_n = 27 ~,~ n = ? $$ | 5 |
| 1044 | Find $ S_{ 32 } $ ( sum of first $ 32 $ terms ) of arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 11 $. | 5 |
| 1045 | Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 12 $. | 5 |
| 1046 | Find $ S_{ 27 } $ ( sum of first $ 27 $ terms ) of arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 11 $. | 5 |
| 1047 | Find $ S_{ 23 } $ ( sum of first $ 23 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 12 $. | 5 |
| 1048 | Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 12 $. | 5 |
| 1049 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 5 $. | 5 |
| 1050 | Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = \frac{ 11 }{ 10 } ~~ \text{and} ~~ d = 2 $. | 5 |
