Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 7901 | Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 1283 ~~ \text{and} ~~ d = -140 $. | 1 |
| 7902 | Find $ a_{ 69 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 6 $. | 1 |
| 7903 | $$ a_1 = -22 ~,~ a_n = 10 ~,~ S_n = 14 ~,~ n = ? $$ | 1 |
| 7904 | $$ a_1 = -15 ~,~ d = -2 ~,~ S_n = 48 ~,~ n = ? $$ | 1 |
| 7905 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = 8 $. | 1 |
| 7906 | Find $ a_{ 504 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $. | 1 |
| 7907 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 4 $. | 1 |
| 7908 | Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 1 $. | 1 |
| 7909 | Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 36 ~~ \text{and} ~~ d = -2 $. | 1 |
| 7910 | Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 79 ~~ \text{and} ~~ d = -\frac{ 32 }{ 5 } $. | 1 |
| 7911 | Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 65 ~~ \text{and} ~~ d = -8 $. | 1 |
| 7912 | Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 26 ~~ \text{and} ~~ d = -\frac{ 4 }{ 5 } $. | 1 |
| 7913 | Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 52 ~~ \text{and} ~~ d = -\frac{ 8 }{ 5 } $. | 1 |
| 7914 | Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = -4 $. | 1 |
| 7915 | Find $ a_{ 63 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 10 } ~~ \text{and} ~~ d = \frac{ 1 }{ 10 } $. | 1 |
| 7916 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $. | 1 |
| 7917 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = \frac{ 28 }{ 5 } ~~ \text{and} ~~ d = \frac{ 9 }{ 5 } $. | 1 |
| 7918 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \frac{ 3 }{ 2 } $. | 1 |
| 7919 | Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $. | 1 |
| 7920 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = -15 ~~ \text{and} ~~ d = 4 $. | 1 |
| 7921 | Find $ a_{ 360 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 1 |
| 7922 | Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 352 ~~ \text{and} ~~ d = -64 $. | 1 |
| 7923 | Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $. | 1 |
| 7924 | $$ a_1 = \frac{ 93 }{ 4 } ~,~ d = \frac{ 1 }{ 4 } ~,~ a_n = 5 ~,~ n = ? $$ | 1 |
| 7925 | Find $ S_{ 59 } $ ( sum of first $ 59 $ terms ) of arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 1 $. | 1 |
| 7926 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 890000 ~~ \text{and} ~~ d = 1000 $. | 1 |
| 7927 | Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = -20 ~~ \text{and} ~~ d = \left( -\frac{ 71 }{ 10 } \right) $. | 1 |
| 7928 | Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \frac{ 54 }{ 5 } $. | 1 |
| 7929 | Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 6 } ~~ \text{and} ~~ d = \frac{ 1 }{ 6 } $. | 1 |
| 7930 | Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 7 } ~~ \text{and} ~~ d = \frac{ 1 }{ 7 } $. | 1 |
| 7931 | Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 7 } ~~ \text{and} ~~ d = \frac{ 1 }{ 7 } $. | 1 |
| 7932 | Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 5 $. | 1 |
| 7933 | Find $ a_{ 42 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 261 $. | 1 |
| 7934 | Find $ S_{ 42 } $ ( sum of first $ 42 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 6 $. | 1 |
| 7935 | Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = 30 $. | 1 |
| 7936 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 10 $. | 1 |
| 7937 | Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -10 \right) $. | 1 |
| 7938 | Find $ a_{ 37 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -10 \right) $. | 1 |
| 7939 | Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 100 $. | 1 |
| 7940 | Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 38 $. | 1 |
| 7941 | Find $ S_{ 47 } $ ( sum of first $ 47 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $. | 1 |
| 7942 | $$ a_1 = 1 ~,~ d = 1 ~,~ a_n = 2017 ~,~ n = ? $$ | 1 |
| 7943 | $$ a_1 = 2 ~,~ d = 2 ~,~ a_n = 2016 ~,~ n = ? $$ | 1 |
| 7944 | Find $ S_{ 672 } $ ( sum of first $ 672 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $. | 1 |
| 7945 | Find $ S_{ 403 } $ ( sum of first $ 403 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $. | 1 |
| 7946 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = \frac{ 8 }{ 3 } ~~ \text{and} ~~ d = \frac{ 8 }{ 21 } $. | 1 |
| 7947 | $$ a_1 = 10 ~~,~~ d = \frac{ 1 }{ 5 } ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 7948 | Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 505 ~~ \text{and} ~~ d = 5 $. | 1 |
| 7949 | Find $ a_{ 3000 } $ of an arithmetic progression if $ a_1 = 12000 ~~ \text{and} ~~ d = 6000 $. | 1 |
| 7950 | Find $ S_{ 3000 } $ ( sum of first $ 3000 $ terms ) of arithmetic progression if $ a_1 = 12000 ~~ \text{and} ~~ d = 6000 $. | 1 |
