Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 1901 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 400 ~~ \text{and} ~~ d = 25 $. | 4 |
| 1902 | Find $ S_{ 187 } $ ( sum of first $ 187 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 2 $. | 4 |
| 1903 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 7 $. | 4 |
| 1904 | Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $. | 4 |
| 1905 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 5 $. | 4 |
| 1906 | Find $ a_{ 36 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 0 $. | 4 |
| 1907 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 4 |
| 1908 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 10 $. | 4 |
| 1909 | Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = \left( -6 \right) $. | 4 |
| 1910 | Find $ S_{ 1000 } $ ( sum of first $ 1000 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 190 $. | 4 |
| 1911 | Find $ S_{ 1250 } $ ( sum of first $ 1250 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 190 $. | 4 |
| 1912 | Find $ a_{ 94 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $. | 4 |
| 1913 | Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \left( -3 \right) $. | 4 |
| 1914 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = \frac{ 2 }{ 5 } ~~ \text{and} ~~ d = \frac{ 2 }{ 5 } $. | 4 |
| 1915 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 200 $. | 4 |
| 1916 | Find $ S_{ 36 } $ ( sum of first $ 36 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 200 $. | 4 |
| 1917 | Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 19 ~~ \text{and} ~~ d = 0 $. | 4 |
| 1918 | Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = 9 $. | 4 |
| 1919 | Find $ a_{ 45 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 2 $. | 4 |
| 1920 | $$ a_1 = 5 ~,~ d = 2 ~,~ S_n = 165 ~,~ n = ? $$ | 4 |
| 1921 | Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 6 $. | 4 |
| 1922 | Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 300 ~~ \text{and} ~~ d = \left( -80 \right) $. | 4 |
| 1923 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 3 ~~ \text{and} ~~ a_{ 5 } = 13 $. | 4 |
| 1924 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 3 ~~ \text{and} ~~ a_{ 8 } = 26 $. | 4 |
| 1925 | $$ a_1 = 2 ~,~ d = 1 ~,~ a_n = 7 ~,~ n = ? $$ | 4 |
| 1926 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 1 $. | 4 |
| 1927 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 2 $. | 4 |
| 1928 | Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 3 $. | 4 |
| 1929 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 3 ~~ \text{and} ~~ a_{ 5 } = 46 $. | 4 |
| 1930 | Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 4 $. | 4 |
| 1931 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 8 $. | 4 |
| 1932 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $. | 4 |
| 1933 | $$ a_{ 7 } = 13 ~~,~~ S_{ 6 } = 27 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 4 |
| 1934 | $$ a_{ 7 } = 14 ~~,~~ S_{ 6 } = 27 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 4 |
| 1935 | $$ a_{ 7 } = 15 ~~,~~ S_{ 6 } = 27 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 4 |
| 1936 | Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = 3 $. | 4 |
| 1937 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 0 $. | 4 |
| 1938 | Find $ a_1 $ (first term of arithmetic progression) if $ d = \frac{ 51 }{ 10 } ~~ \text{and} ~~ a_{ 8 } = 50 $. | 4 |
| 1939 | $$ a_1 = -2 ~,~ d = 5 ~,~ a_n = 43 ~,~ n = ? $$ | 4 |
| 1940 | Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $. | 4 |
| 1941 | Find $ S_{ 48 } $ ( sum of first $ 48 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $. | 4 |
| 1942 | Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 55 ~~ \text{and} ~~ d = 950 $. | 4 |
| 1943 | Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $. | 4 |
| 1944 | Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 189 $. | 4 |
| 1945 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $. | 4 |
| 1946 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $. | 4 |
| 1947 | Find $ a_{ 47 } $ of an arithmetic progression if $ a_1 = \frac{ 2 }{ 5 } ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 6 } \right) $. | 3 |
| 1948 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 2 ~~ \text{and} ~~ a_{ 4 } = 12 $. | 3 |
| 1949 | Find $ a_{ 91 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 2 $. | 3 |
| 1950 | Find $ d $ (common difference of arithmetic progression) if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ S_{ 30 } = 1350 $. | 3 |
