Arithmetic sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Arithmetic sequences.
| ID |
Problem |
Count |
| 2001 | Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 8 $. | 3 |
| 2002 | Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 8 $. | 3 |
| 2003 | Find $ a_{ 130 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $. | 3 |
| 2004 | Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 1 $. | 3 |
| 2005 | Find $ a_{ 1000 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \frac{ 1 }{ 20 } $. | 3 |
| 2006 | Find $ S_{ 40 } $ ( sum of first $ 40 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 1000 $. | 3 |
| 2007 | Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -2 \right) $. | 3 |
| 2008 | Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $. | 3 |
| 2009 | Find $ a_{ 32 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 3 $. | 3 |
| 2010 | Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = 3 $. | 3 |
| 2011 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 6 $. | 3 |
| 2012 | $$ a_1 = 2 ~,~ d = 2 ~,~ S_n = 20 ~,~ n = ? $$ | 3 |
| 2013 | Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 5 $. | 3 |
| 2014 | Find $ S_{ 9 } $ ( sum of first $ 9 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $. | 3 |
| 2015 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = -4 ~~ \text{and} ~~ d = 0 $. | 3 |
| 2016 | Find $ S_{ 400 } $ ( sum of first $ 400 $ terms ) of arithmetic progression if $ a_1 = 302 ~~ \text{and} ~~ d = 29 $. | 3 |
| 2017 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 200 $. | 3 |
| 2018 | Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $. | 3 |
| 2019 | $$ a_1 = 250 ~,~ d = 75 ~,~ a_n = 2000 ~,~ n = ? $$ | 3 |
| 2020 | Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 0.625 ~~ \text{and} ~~ d = -4 $. | 3 |
| 2021 | Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $. | 3 |
| 2022 | Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 859 ~~ \text{and} ~~ d = 1 $. | 3 |
| 2023 | Find $ S_{ 110 } $ ( sum of first $ 110 $ terms ) of arithmetic progression if $ a_1 = 849 ~~ \text{and} ~~ d = 1 $. | 3 |
| 2024 | Find $ S_{ 302 } $ ( sum of first $ 302 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $. | 3 |
| 2025 | Find $ a_{ 98 } $ of an arithmetic progression if $ a_1 = -40 ~~ \text{and} ~~ d = 2 $. | 3 |
| 2026 | Find $ S_{ 90 } $ ( sum of first $ 90 $ terms ) of arithmetic progression if $ a_1 = -40 ~~ \text{and} ~~ d = 2 $. | 3 |
| 2027 | $$ a_1 = 3 ~,~ d = 2 ~,~ S_n = \frac{ 2703 }{ 2 } ~,~ n = ? $$ | 3 |
| 2028 | Find $ S_{ 2 } $ ( sum of first $ 2 $ terms ) of arithmetic progression if $ a_1 = 150 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 3 |
| 2029 | Find $ S_{ 2 } $ ( sum of first $ 2 $ terms ) of arithmetic progression if $ a_1 = 75 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $. | 3 |
| 2030 | Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = \left( -7 \right) $. | 3 |
| 2031 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 0 $. | 3 |
| 2032 | Find $ S_{ 101 } $ ( sum of first $ 101 $ terms ) of arithmetic progression if $ a_1 = 150 ~~ \text{and} ~~ d = 150 $. | 3 |
| 2033 | Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 93 $. | 3 |
| 2034 | Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = -21 ~~ \text{and} ~~ d = 7 $. | 3 |
| 2035 | Find $ a_1 $ (first term of arithmetic progression) if $ d = -5 ~~ \text{and} ~~ a_{ 8 } = -32 $. | 3 |
| 2036 | Find $ a_{ 1196 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 4 $. | 3 |
| 2037 | Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 1000 $. | 3 |
| 2038 | Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = -37 ~~ \text{and} ~~ d = 6 $. | 3 |
| 2039 | Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 11 $. | 3 |
| 2040 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 4 $. | 3 |
| 2041 | Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -80 ~~ \text{and} ~~ d = 5 $. | 3 |
| 2042 | Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 900 ~~ \text{and} ~~ d = 75 $. | 3 |
| 2043 | Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 2 $. | 3 |
| 2044 | Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 4 $. | 3 |
| 2045 | $$ a_1 = 14 ~,~ d = -3 ~,~ a_n = -82 ~,~ n = ? $$ | 3 |
| 2046 | Find $ a_{ 2 } $ of an arithmetic progression if $ a_1 = \frac{ 7 }{ 3 } ~~ \text{and} ~~ d = \left( -\frac{ 10 }{ 3 } \right) $. | 3 |
| 2047 | Find $ S_{ 60 } $ ( sum of first $ 60 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 6 $. | 3 |
| 2048 | Find $ a_{ 112 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $. | 3 |
| 2049 | Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 120 ~~ \text{and} ~~ d = 5 $. | 3 |
| 2050 | Find $ S_{ 75 } $ ( sum of first $ 75 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 5 $. | 3 |
