Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 1951 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \left( -3 \right) $. | 3 |
| 1952 | Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $. | 3 |
| 1953 | Find $ S_{ 2026 } $ ( sum of first $ 2026 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 1 $. | 3 |
| 1954 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 6 $. | 3 |
| 1955 | Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $. | 3 |
| 1956 | Find $ S_{ 102 } $ ( sum of first $ 102 $ terms ) of arithmetic progression if $ a_1 = 599 ~~ \text{and} ~~ d = -6 $. | 3 |
| 1957 | Find common difference $ d $ of arithmetic progression if $ a_1 = \frac{ 17 }{ 10 } ~~ \text{and} ~~ a_{ 4 } = 17 $. | 3 |
| 1958 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = \frac{ 17 }{ 10 } ~~ \text{and} ~~ d = \frac{ 51 }{ 10 } $. | 3 |
| 1959 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 17 }{ 10 } ~~ \text{and} ~~ d = \frac{ 51 }{ 10 } $. | 3 |
| 1960 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 1 $. | 3 |
| 1961 | Find $ a_{ 2609 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $. | 3 |
| 1962 | Find $ S_{ 500 } $ ( sum of first $ 500 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $. | 3 |
| 1963 | Find $ S_{ 48 } $ ( sum of first $ 48 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $. | 3 |
| 1964 | Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 6 $. | 3 |
| 1965 | Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 3 $. | 3 |
| 1966 | Find $ S_{ 28 } $ ( sum of first $ 28 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 3 |
| 1967 | Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 1 $. | 3 |
| 1968 | Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = \left( -12 \right) $. | 3 |
| 1969 | Find $ a_{ 36 } $ of an arithmetic progression if $ a_1 = -56 ~~ \text{and} ~~ d = 0 $. | 3 |
| 1970 | Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 120 ~~ \text{and} ~~ d = 12 $. | 3 |
| 1971 | $$ a_1 = 2 ~,~ d = \frac{ 5 }{ 2 } ~,~ a_n = 2 ~,~ n = ? $$ | 3 |
| 1972 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 5 $. | 3 |
| 1973 | Find $ S_{ 69 } $ ( sum of first $ 69 $ terms ) of arithmetic progression if $ a_1 = 76 ~~ \text{and} ~~ d = 2 $. | 3 |
| 1974 | Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = -\frac{ 1 }{ 3 } $. | 3 |
| 1975 | Find $ a_{ 28 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 3 |
| 1976 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = \frac{ 2 }{ 5 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 3 |
| 1977 | Find $ S_{ 24 } $ ( sum of first $ 24 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 200 $. | 3 |
| 1978 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 10 }{ 11 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 11 } \right) $. | 3 |
| 1979 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 219 }{ 2 } ~~ \text{and} ~~ d = \left( -\frac{ 9 }{ 2 } \right) $. | 3 |
| 1980 | Find $ a_{ 11 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $. | 3 |
| 1981 | Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $. | 3 |
| 1982 | $$ a_1 = 16 ~,~ d = -3 ~,~ S_n = -6 ~,~ n = ? $$ | 3 |
| 1983 | Find $ a_{ 690 } $ of an arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 96 $. | 3 |
| 1984 | Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $. | 3 |
| 1985 | Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 1 $. | 3 |
| 1986 | Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 6 $. | 3 |
| 1987 | Find common difference $ d $ of arithmetic progression if $ a_1 = \frac{ 1 }{ 3 } ~~ \text{and} ~~ a_{ 2 } = \frac{ 11 }{ 24 } $. | 3 |
| 1988 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = \frac{ 2 }{ 5 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $. | 3 |
| 1989 | Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 5000 ~~ \text{and} ~~ d = 5000 $. | 3 |
| 1990 | $$ a_{ 7 } = 12 ~~,~~ S_{ 6 } = 27 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 3 |
| 1991 | Find $ a_{ 1000 } $ of an arithmetic progression if $ a_1 = -1000 ~~ \text{and} ~~ d = 1 $. | 3 |
| 1992 | Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 36 ~~ \text{and} ~~ d = -6 $. | 3 |
| 1993 | Find common difference $ d $ of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ a_{ 4 } = -8 $. | 3 |
| 1994 | $$ a_1 = 6 ~,~ d = 6 ~,~ a_n = 600 ~,~ n = ? $$ | 3 |
| 1995 | Find $ S_{ 69 } $ ( sum of first $ 69 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $. | 3 |
| 1996 | Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = -13 ~~ \text{and} ~~ d = \left( -10 \right) $. | 3 |
| 1997 | $$ a_1 = 5 ~,~ d = 2 ~,~ S_n = 192 ~,~ n = ? $$ | 3 |
| 1998 | Find $ a_{ 1000 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \left( -2 \right) $. | 3 |
| 1999 | $$ a_1 = -30 ~,~ d = -100 ~,~ a_n = 38 ~,~ n = ? $$ | 3 |
| 2000 | Find $ S_{ 44 } $ ( sum of first $ 44 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $. | 3 |
