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
4351	$$ a_1 = 2 ~,~ d = 3 ~,~ S_n = 100 ~,~ n = ? $$	2
4352	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = \left( -7 \right) $.	2
4353	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = -20 ~~ \text{and} ~~ d = 2 $.	2
4354	Find $ S_{ 2017 } $ ( sum of first $ 2017 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	2
4355	$$ a_1 = 1 ~,~ d = 1 ~,~ S_n = 450 ~,~ n = ? $$	2
4356	Find $ a_{ 9400 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
4357	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	2
4358	Find $ a_{ 31 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	2
4359	$$ a_1 = -36 ~,~ d = 5 ~,~ a_n = 14 ~,~ n = ? $$	2
4360	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 7 $.	2
4361	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 7 $.	2
4362	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 6 $.	2
4363	Find $ S_{ 370 } $ ( sum of first $ 370 $ terms ) of arithmetic progression if $ a_1 = 13100000 ~~ \text{and} ~~ d = 100000 $.	2
4364	Find $ S_{ 3 } $ ( sum of first $ 3 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 4 $.	2
4365	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = \left( -4 \right) $.	2
4366	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $.	2
4367	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $.	2
4368	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 9 $.	2
4369	Find $ a_{ 5050 } $ of an arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 1 $.	2
4370	Find $ S_{ 25 } $ ( sum of first $ 25 $ terms ) of arithmetic progression if $ a_1 = 15 ~~ \text{and} ~~ d = -5 $.	2
4371	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = -8 ~~ \text{and} ~~ d = 4 $.	2
4372	Find $ S_{ 0 } $ ( sum of first $ 0 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 7 $.	2
4373	Find $ S_{ 7 } $ ( sum of first $ 7 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 7 $.	2
4374	$$ a_1 = 25 ~,~ d = 7 ~,~ S_n = 322 ~,~ n = ? $$	2
4375	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 8 $.	2
4376	Find $ S_{ 41 } $ ( sum of first $ 41 $ terms ) of arithmetic progression if $ a_1 = 14 ~~ \text{and} ~~ d = 8 $.	2
4377	Find $ S_{ 8 } $ ( sum of first $ 8 $ terms ) of arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
4378	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 1200 ~~ \text{and} ~~ d = 90 $.	2
4379	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = -32 ~~ \text{and} ~~ d = 17 $.	2
4380	Find $ a_{ 16 } $ of an arithmetic progression if $ a_1 = 379000 ~~ \text{and} ~~ d = \frac{ 27 }{ 100 } $.	2
4381	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = 88 ~~ \text{and} ~~ d = -12 $.	2
4382	Find $ S_{ 98 } $ ( sum of first $ 98 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $.	2
4383	Find $ S_{ 99 } $ ( sum of first $ 99 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 5 $.	2
4384	Find $ S_{ 4 } $ ( sum of first $ 4 $ terms ) of arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = -13 $.	2
4385	Find $ a_{ 1413 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = 200 $.	2
4386	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 50 ~~ \text{and} ~~ d = 4 $.	2
4387	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 7 $.	2
4388	Find $ a_{ 23 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 3 $.	2
4389	Find $ a_{ 3 } $ of an arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = \frac{ 1 }{ 2 } $.	2
4390	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = \frac{ 1 }{ 4 } ~~ \text{and} ~~ d = \frac{ 1 }{ 4 } $.	2
4391	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 64 ~~ \text{and} ~~ d = 8 $.	2
4392	Find $ S_{ 11 } $ ( sum of first $ 11 $ terms ) of arithmetic progression if $ a_1 = 64 ~~ \text{and} ~~ d = -8 $.	2
4393	Find $ a_1 $ (first term of arithmetic progression) if $ d = -\frac{ 3 }{ 2 } ~~ \text{and} ~~ a_{ 9 } = 4 $.	2
4394	Find $ a_{ 150 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = \left( -\frac{ 1 }{ 2 } \right) $.	2
4395	Find $ S_{ 30 } $ ( sum of first $ 30 $ terms ) of arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 500 $.	2
4396	Find $ S_{ 70 } $ ( sum of first $ 70 $ terms ) of arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 500 $.	2
4397	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 500 ~~ \text{and} ~~ d = 500 $.	2
4398	$$ a_1 = 35 ~,~ d = 1 ~,~ S_n = 1000 ~,~ n = ? $$	2
4399	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 20 ~~ \text{and} ~~ d = 5 $.	2
4400	Find $ a_{ 500 } $ of an arithmetic progression if $ a_1 = 24 ~~ \text{and} ~~ d = 2 $.	2