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
8651	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -13 \right) $.	1
8652	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = -13 $.	1
8653	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = -10 $.	1
8654	Find $ a_{ 21 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = \left( -10 \right) $.	1
8655	Find $ S_{ 21 } $ ( sum of first $ 21 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = -10 $.	1
8656	Find $ a_{ 89 } $ of an arithmetic progression if $ a_1 = 38 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
8657	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 38 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
8658	Find $ a_{ 89 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
8659	Find $ a_{ 89 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
8660	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = \left( -8 \right) $.	1
8661	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -8 \right) $.	1
8662	Find $ a_{ 35 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = \left( -8 \right) $.	1
8663	Find $ a_{ 56 } $ of an arithmetic progression if $ a_1 = -\frac{ 4 }{ 5 } ~~ \text{and} ~~ d = \frac{ 3 }{ 5 } $.	1
8664	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 6 $.	1
8665	Find $ a_{ 1000 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -9 \right) $.	1
8666	Find $ a_{ 2024 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
8667	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	1
8668	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = -\frac{ 8 }{ 9 } ~~ \text{and} ~~ d = \frac{ 88 }{ 27 } $.	1
8669	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 6 $.	1
8670	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -6 \right) $.	1
8671	Find $ S_{ 38 } $ ( sum of first $ 38 $ terms ) of arithmetic progression if $ a_1 = 1000 ~~ \text{and} ~~ d = 1000 $.	1
8672	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 14 $.	1
8673	Find $ a_1 $ (first term of arithmetic progression) if $ d = 6 ~~ \text{and} ~~ a_{ 23 } = 33 $.	1
8674	Find $ S_{ 34 } $ ( sum of first $ 34 $ terms ) of arithmetic progression if $ a_1 = -99 ~~ \text{and} ~~ d = 6 $.	1
8675	$$ a_1 = 4 ~,~ d = 6 ~,~ a_n = 14 ~,~ n = ? $$	1
8676	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 1 $.	1
8677	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 59 ~~ \text{and} ~~ d = 5 $.	1
8678	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = -103 ~~ \text{and} ~~ d = -7 $.	1
8679	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 207 ~~ \text{and} ~~ d = 332 $.	1
8680	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 32 $.	1
8681	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 82 ~~ \text{and} ~~ d = -6 $.	1
8682	Find $ a_{ 49 } $ of an arithmetic progression if $ a_1 = \frac{ 43 }{ 2 } ~~ \text{and} ~~ d = \frac{ 43 }{ 2 } $.	1
8683	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 3 $.	1
8684	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 8 $.	1
8685	Find $ a_{ 26 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 3 $.	1
8686	Find $ a_{ 25 } $ of an arithmetic progression if $ a_1 = \frac{ 445 }{ 4 } ~~ \text{and} ~~ d = \frac{ 25 }{ 4 } $.	1
8687	Find $ S_{ 48 } $ ( sum of first $ 48 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	1
8688	Find $ S_{ 48 } $ ( sum of first $ 48 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $.	1
8689	Find $ S_{ 47 } $ ( sum of first $ 47 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 4 $.	1
8690	Find $ S_{ 45 } $ ( sum of first $ 45 $ terms ) of arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 4 $.	1
8691	Find $ S_{ 33 } $ ( sum of first $ 33 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 9 $.	1
8692	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 44 ~~ \text{and} ~~ d = 18 $.	1
8693	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = 5 $.	1
8694	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -1 \right) $.	1
8695	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	1
8696	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = \frac{ 13 }{ 5 } $.	1
8697	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 4567 ~~ \text{and} ~~ d = 1111 $.	1
8698	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 13 $.	1
8699	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	1
8700	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 7 $.	1