Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 7801 | Find $ a_{ 62 } $ of an arithmetic progression if $ a_1 = -894 ~~ \text{and} ~~ d = 15 $. | 1 |
| 7802 | Find common difference $ d $ of arithmetic progression if $ a_1 = 36 ~~ \text{and} ~~ a_{ 63 } = 966 $. | 1 |
| 7803 | Find $ a_{ 78 } $ of an arithmetic progression if $ a_1 = -189 ~~ \text{and} ~~ d = 15 $. | 1 |
| 7804 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 15 ~~ \text{and} ~~ a_{ 78 } = 966 $. | 1 |
| 7805 | $$ a_1 = 48500 ~,~ d = 1200 ~,~ S_n = 321000 ~,~ n = ? $$ | 1 |
| 7806 | $$ a_1 = -1 ~,~ a_n = 58 ~,~ S_n = 456 ~,~ n = ? $$ | 1 |
| 7807 | $$ a_1 = -70 ~,~ d = 840 ~,~ S_n = 21 ~,~ n = ? $$ | 1 |
| 7808 | Find $ d $ (common difference of arithmetic progression) if $ a_1 = -51 ~~ \text{and} ~~ S_{ 22 } = 726 $. | 1 |
| 7809 | Find $ a_{ 34 } $ of an arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = 8 $. | 1 |
| 7810 | Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = -19 ~~ \text{and} ~~ d = \left( -2 \right) $. | 1 |
| 7811 | $$ a_1 = -12 ~,~ d = -5 ~,~ a_n = 40 ~,~ n = ? $$ | 1 |
| 7812 | $$ a_1 = -24 ~,~ d = 10 ~,~ a_n = 21 ~,~ n = ? $$ | 1 |
| 7813 | $$ a_1 = -3 ~,~ d = 2 ~,~ S_n = -224 ~,~ n = ? $$ | 1 |
| 7814 | $$ a_1 = 29 ~,~ d = -200 ~,~ a_n = 32 ~,~ n = ? $$ | 1 |
| 7815 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 4 ~~ \text{and} ~~ a_{ 6 } = 0 $. | 1 |
| 7816 | Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $. | 1 |
| 7817 | Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -6 \right) $. | 1 |
| 7818 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 5 $. | 1 |
| 7819 | Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = 1 $. | 1 |
| 7820 | Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 6 } $. | 1 |
| 7821 | Find $ S_{ 3 } $ ( sum of first $ 3 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \frac{ 1 }{ 10 } $. | 1 |
| 7822 | $$ a_{ 2 } = 2 ~~,~~ S_{ 7 } = 24 ~~,~~ a_1 = ? ~~,~~ d = ? $$ | 1 |
| 7823 | Find $ S_{ 300 } $ ( sum of first $ 300 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 14 $. | 1 |
| 7824 | Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = -33 ~~ \text{and} ~~ d = -5 $. | 1 |
| 7825 | Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 4 $. | 1 |
| 7826 | Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 4 $. | 1 |
| 7827 | Find $ a_{ 38 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 4 $. | 1 |
| 7828 | Find $ S_{ 38 } $ ( sum of first $ 38 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 4 $. | 1 |
| 7829 | Find $ a_{ 18 } $ of an arithmetic progression if $ a_1 = -54 ~~ \text{and} ~~ d = 7 $. | 1 |
| 7830 | $$ a_1 = -15 ~,~ d = 7 ~,~ S_n = -256 ~,~ n = ? $$ | 1 |
| 7831 | $$ a_1 = 10 ~,~ d = 4 ~,~ S_n = 162 ~,~ n = ? $$ | 1 |
| 7832 | $$ a_1 = 5 ~,~ d = 3 ~,~ S_n = 165 ~,~ n = ? $$ | 1 |
| 7833 | $$ a_1 = 10 ~,~ d = 4 ~,~ S_n = 3034 ~,~ n = ? $$ | 1 |
| 7834 | Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 60 ~~ \text{and} ~~ d = \frac{ 5 }{ 2 } $. | 1 |
| 7835 | Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -2 \right) $. | 1 |
| 7836 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = -3 ~~ \text{and} ~~ d = -4 $. | 1 |
| 7837 | Find common difference $ d $ of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ a_{ 30 } = 121 $. | 1 |
| 7838 | Find $ a_1 $ (first term of arithmetic progression) if $ d = 4 ~~ \text{and} ~~ S_{ 16 } = 464 $. | 1 |
| 7839 | Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 550 ~~ \text{and} ~~ d = 50 $. | 1 |
| 7840 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 24 }{ 5 } ~~ \text{and} ~~ d = \frac{ 14 }{ 5 } $. | 1 |
| 7841 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = \frac{ 24 }{ 5 } ~~ \text{and} ~~ d = \frac{ 14 }{ 5 } $. | 1 |
| 7842 | $$ a_1 = \frac{ 24 }{ 5 } ~,~ d = \frac{ 14 }{ 5 } ~,~ S_n = 1000 ~,~ n = ? $$ | 1 |
| 7843 | Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -2 \right) $. | 1 |
| 7844 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -2 \right) $. | 1 |
| 7845 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -2 \right) $. | 1 |
| 7846 | Find $ a_{ 135 } $ of an arithmetic progression if $ a_1 = 26 ~~ \text{and} ~~ d = 18 $. | 1 |
| 7847 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -2 \right) $. | 1 |
| 7848 | Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \frac{ 2 }{ 3 } $. | 1 |
| 7849 | Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 6 $. | 1 |
| 7850 | Find $ a_{ 40 } $ of an arithmetic progression if $ a_1 = -30 ~~ \text{and} ~~ d = \left( -100 \right) $. | 1 |
