Arithmetic sequences

(the database of solved problems)

All the problems and solutions shown below were generated using the Arithmetic sequences.

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ID	Problem	Count
5751	$$ a_1 = 16 ~,~ d = -9 ~,~ a_n = 18 ~,~ n = ? $$	2
5752	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = -19 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
5753	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 78 $.	2
5754	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = -4 $.	2
5755	Find $ S_{ 333 } $ ( sum of first $ 333 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	2
5756	Find $ a_{ 90 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 35 $.	2
5757	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 1250 ~~ \text{and} ~~ d = 750 $.	2
5758	Find $ S_{ 4463 } $ ( sum of first $ 4463 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 100 $.	2
5759	Find $ a_{ 255 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 10 $.	2
5760	Find $ S_{ 255 } $ ( sum of first $ 255 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 25 $.	2
5761	Find $ a_{ 255 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 50 $.	2
5762	Find $ S_{ 255 } $ ( sum of first $ 255 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 20 $.	2
5763	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 0 $.	2
5764	Find $ S_{ 1 } $ ( sum of first $ 1 $ terms ) of arithmetic progression if $ a_1 = 3125 ~~ \text{and} ~~ d = \frac{ 1 }{ 5 } $.	2
5765	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 230 ~~ \text{and} ~~ d = \left( -60 \right) $.	2
5766	Find $ a_{ 200 } $ of an arithmetic progression if $ a_1 = -30 ~~ \text{and} ~~ d = 5 $.	2
5767	Find $ S_{ 140 } $ ( sum of first $ 140 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
5768	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	2
5769	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 26000 ~~ \text{and} ~~ d = 1500 $.	2
5770	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 26000 ~~ \text{and} ~~ d = 1500 $.	2
5771	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 28000 ~~ \text{and} ~~ d = 800 $.	2
5772	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 4565 ~~ \text{and} ~~ d = 226 $.	2
5773	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 4581 ~~ \text{and} ~~ d = 224 $.	2
5774	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 33000 ~~ \text{and} ~~ d = 2000 $.	2
5775	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 28000 ~~ \text{and} ~~ d = 2800 $.	2
5776	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 37000 ~~ \text{and} ~~ d = 700 $.	2
5777	Find $ S_{ 34 } $ ( sum of first $ 34 $ terms ) of arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 5 $.	2
5778	Find $ a_{ 122 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	2
5779	$$ a_1 = 5 ~,~ d = -4 ~,~ a_n = -107 ~,~ n = ? $$	2
5780	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 28000 ~~ \text{and} ~~ d = \frac{ 1 }{ 20 } $.	2
5781	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = \frac{ 73 }{ 100 } $.	2
5782	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 0 $.	2
5783	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 108000 ~~ \text{and} ~~ d = 36000 $.	2
5784	Find $ a_{ 255 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 20 $.	2
5785	Find $ a_{ 45 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $.	2
5786	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = -3 $.	2
5787	$$ a_1 = 3 ~,~ a_n = 21 ~,~ S_n = 29 ~,~ n = ? $$	2
5788	Find $ a_{ 70 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 7 $.	2
5789	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = \frac{ 312 }{ 5 } ~~ \text{and} ~~ d = -\frac{ 1 }{ 10 } $.	2
5790	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = -1 ~~ \text{and} ~~ d = 16 $.	2
5791	Find $ a_1 $ (first term of arithmetic progression) if $ d = 9 ~~ \text{and} ~~ S_{ 33 } = 5016 $.	2
5792	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = -\frac{ 15 }{ 2 } ~~ \text{and} ~~ d = 2 $.	2
5793	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = -9 $.	2
5794	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 10 $.	2
5795	Find $ a_1 $ (first term of arithmetic progression) if $ d = 4 ~~ \text{and} ~~ a_{ 3 } = 5 $.	2
5796	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
5797	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = \left( -6 \right) $.	2
5798	Find $ a_{ 96 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -5 \right) $.	2
5799	$$ a_1 = 1 ~,~ d = 3 ~,~ a_n = 21 ~,~ n = ? $$	2
5800	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 1105 ~~ \text{and} ~~ d = 20 $.	2