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
10351	Find $ a_{ 80 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 7 $.	1
10352	Find $ a_{ 222 } $ of an arithmetic progression if $ a_1 = \frac{ 52 }{ 5 } ~~ \text{and} ~~ d = 0.3495 $.	1
10353	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = 0 $.	1
10354	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	1
10355	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 2 } ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	1
10356	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	1
10357	Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = 552 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
10358	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = \left( -2 \right) $.	1
10359	Find $ S_{ 41 } $ ( sum of first $ 41 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 7 $.	1
10360	Find $ S_{ 19 } $ ( sum of first $ 19 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 5 $.	1
10361	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = 6 $.	1
10362	Find $ a_{ 1 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 2 $.	1
10363	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 9 $.	1
10364	$$ a_{ 2 } = 2 ~~,~~ S_{ 47 } = 2 ~~,~~ a_1 = ? ~~,~~ d = ? $$	1
10365	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = -\frac{ 4 }{ 5 } $.	1
10366	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 7 $.	1
10367	Find $ a_{ 45 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -7 \right) $.	1
10368	Find $ a_{ 168 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 0 $.	1
10369	Find $ a_1 $ (first term of arithmetic progression) if $ d = 5 ~~ \text{and} ~~ a_{ 23 } = 104 $.	1
10370	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 21 ~~ \text{and} ~~ d = 2 $.	1
10371	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = -32 $.	1
10372	Find $ a_{ 19 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 7 $.	1
10373	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 47697 ~~ \text{and} ~~ d = -576 $.	1
10374	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
10375	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	1
10376	$$ a_1 = -6 ~,~ d = 4 ~,~ a_n = 50 ~,~ n = ? $$	1
10377	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 11 $.	1
10378	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 1 $.	1
10379	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = -21 ~~ \text{and} ~~ d = 5 $.	1
10380	$$ a_1 = -26 ~,~ d = -11 ~,~ a_n = 20 ~,~ n = ? $$	1
10381	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 8 $.	1
10382	Find $ S_{ 2019 } $ ( sum of first $ 2019 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	1
10383	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 44 ~~ \text{and} ~~ d = -7 $.	1
10384	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 5 $.	1
10385	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $.	1
10386	Find $ S_{ 48 } $ ( sum of first $ 48 $ terms ) of arithmetic progression if $ a_1 = -29 ~~ \text{and} ~~ d = 2 $.	1
10387	Find $ a_{ 26 } $ of an arithmetic progression if $ a_1 = 49 ~~ \text{and} ~~ d = \left( -3 \right) $.	1
10388	Find $ S_{ 26 } $ ( sum of first $ 26 $ terms ) of arithmetic progression if $ a_1 = 49 ~~ \text{and} ~~ d = -3 $.	1
10389	Find $ S_{ 180 } $ ( sum of first $ 180 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $.	1
10390	Find $ S_{ 180 } $ ( sum of first $ 180 $ terms ) of arithmetic progression if $ a_1 = 200 ~~ \text{and} ~~ d = 200 $.	1
10391	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 9 $.	1
10392	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 4 $.	1
10393	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 4 $.	1
10394	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 41 ~~ \text{and} ~~ d = 0 $.	1
10395	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = -3 $.	1
10396	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 4 $.	1
10397	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
10398	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = \left( -5 \right) $.	1
10399	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 5000 ~~ \text{and} ~~ d = 7500 $.	1
10400	Find $ a_{ 300 } $ of an arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = \frac{ 3 }{ 5 } $.	1