Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 2051 | Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 18000 ~~ \text{and} ~~ d = -500 $. | 3 |
| 2052 | Find $ S_{ 31 } $ ( sum of first $ 31 $ terms ) of arithmetic progression if $ a_1 = 18000 ~~ \text{and} ~~ d = 500 $. | 3 |
| 2053 | $$ a_1 = 7 ~,~ d = 3 ~,~ a_n = 394 ~,~ n = ? $$ | 3 |
| 2054 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $. | 3 |
| 2055 | Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = -6 $. | 3 |
| 2056 | Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = -17 ~~ \text{and} ~~ d = 10 $. | 3 |
| 2057 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 4 $. | 3 |
| 2058 | Find $ S_{ 354 } $ ( sum of first $ 354 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 3 |
| 2059 | Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 22840 ~~ \text{and} ~~ d = 63 $. | 3 |
| 2060 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 22840 ~~ \text{and} ~~ d = 63 $. | 3 |
| 2061 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 93 ~~ \text{and} ~~ d = 93 $. | 3 |
| 2062 | Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 40 ~~ \text{and} ~~ d = -6 $. | 3 |
| 2063 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 40 ~~ \text{and} ~~ d = -6 $. | 3 |
| 2064 | Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 40 ~~ \text{and} ~~ d = -6 $. | 3 |
| 2065 | Find $ S_{ 45 } $ ( sum of first $ 45 $ terms ) of arithmetic progression if $ a_1 = 40 ~~ \text{and} ~~ d = -6 $. | 3 |
| 2066 | Find $ S_{ 42 } $ ( sum of first $ 42 $ terms ) of arithmetic progression if $ a_1 = 40 ~~ \text{and} ~~ d = -6 $. | 3 |
| 2067 | Find $ a_{ 26 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 13 $. | 3 |
| 2068 | Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = -31 ~~ \text{and} ~~ d = -7 $. | 3 |
| 2069 | Find $ S_{ 64 } $ ( sum of first $ 64 $ terms ) of arithmetic progression if $ a_1 = 1960 ~~ \text{and} ~~ d = 1 $. | 3 |
| 2070 | Find $ S_{ 60 } $ ( sum of first $ 60 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $. | 3 |
| 2071 | Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $. | 3 |
| 2072 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 42 ~~ \text{and} ~~ d = 0 $. | 3 |
| 2073 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 4 $. | 3 |
| 2074 | $$ a_1 = 201816 ~,~ d = 2 ~,~ S_n = -2 ~,~ n = ? $$ | 3 |
| 2075 | Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 9 $. | 3 |
| 2076 | Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = \left( -4 \right) $. | 3 |
| 2077 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 3 $. | 3 |
| 2078 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 3 $. | 3 |
| 2079 | Find $ a_{ 99 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $. | 3 |
| 2080 | Find $ a_{ 54 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = \left( -11 \right) $. | 3 |
| 2081 | Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $. | 3 |
| 2082 | Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 12 $. | 3 |
| 2083 | $$ a_{ 5 } = 41 ~~,~~ S_{ 5 } = 145 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 3 |
| 2084 | Find $ a_{ 39 } $ of an arithmetic progression if $ a_1 = -\frac{ 3 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 3 |
| 2085 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 4 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $. | 3 |
| 2086 | Find $ a_{ 74 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = \left( -8 \right) $. | 3 |
| 2087 | Find $ a_{ 120 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $. | 3 |
| 2088 | Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = \left( -5 \right) $. | 3 |
| 2089 | Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = \left( -10 \right) $. | 3 |
| 2090 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -34 ~~ \text{and} ~~ d = 10 $. | 3 |
| 2091 | Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 10 $. | 3 |
| 2092 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -5 \right) $. | 3 |
| 2093 | Find $ a_{ 85 } $ of an arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = \left( -4 \right) $. | 3 |
| 2094 | Find $ a_{ 68 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 5 $. | 3 |
| 2095 | Find $ a_{ 62 } $ of an arithmetic progression if $ a_1 = \frac{ 7 }{ 2 } ~~ \text{and} ~~ d = \frac{ 11 }{ 2 } $. | 3 |
| 2096 | Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 2 $. | 3 |
| 2097 | Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 7 $. | 3 |
| 2098 | $$ a_1 = 36 ~,~ d = -4 ~,~ a_n = 4 ~,~ n = ? $$ | 3 |
| 2099 | Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = -20 ~~ \text{and} ~~ d = 2 $. | 3 |
| 2100 | Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 30 ~~ \text{and} ~~ d = 6 $. | 3 |
