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
151	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $.	11
152	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 2 $.	11
153	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 4 $.	10
154	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $.	10
155	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	10
156	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	10
157	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 5 $.	10
158	Find $ a_{ 26 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 2 $.	10
159	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = -6 ~~ \text{and} ~~ d = \left( -3 \right) $.	10
160	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $.	10
161	$$ a_1 = 15 ~,~ a_n = 79 ~,~ S_n = 423 ~,~ n = ? $$	10
162	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	10
163	Find $ S_{ 16 } $ ( sum of first $ 16 $ terms ) of arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 12 $.	10
164	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	10
165	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 32 ~~ \text{and} ~~ d = 5 $.	10
166	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 5 $.	10
167	Find $ S_{ 600 } $ ( sum of first $ 600 $ terms ) of arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 6 $.	10
168	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $.	10
169	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	10
170	Find $ a_{ 72 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = \left( -4 \right) $.	10
171	Find $ S_{ 500 } $ ( sum of first $ 500 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	10
172	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = -21 ~~ \text{and} ~~ d = 7 $.	10
173	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	10
174	Find $ S_{ 5 } $ ( sum of first $ 5 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 2 $.	10
175	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	10
176	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 4 $.	10
177	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 4 $.	10
178	Find $ a_{ 38 } $ of an arithmetic progression if $ a_1 = 211 ~~ \text{and} ~~ d = \left( -4 \right) $.	10
179	Find $ a_{ 14 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 7 $.	10
180	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	10
181	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = 10 $.	10
182	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	10
183	Find $ a_{ 87 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 13 $.	10
184	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 3 $.	10
185	Find $ S_{ 34 } $ ( sum of first $ 34 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	10
186	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 40 ~~ \text{and} ~~ d = \left( -4 \right) $.	10
187	Find $ a_{ 82 } $ of an arithmetic progression if $ a_1 = -10 ~~ \text{and} ~~ d = 16 $.	10
188	Find $ a_{ 68 } $ of an arithmetic progression if $ a_1 = -19 ~~ \text{and} ~~ d = \left( -14 \right) $.	10
189	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	10
190	Find $ S_{ 1000 } $ ( sum of first $ 1000 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	10
191	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 0 ~~ \text{and} ~~ d = 1 $.	10
192	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	10
193	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 3 $.	9
194	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 4 $.	9
195	Find $ S_{ 180 } $ ( sum of first $ 180 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	9
196	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 2 $.	9
197	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = -30 ~~ \text{and} ~~ d = \left( -2 \right) $.	9
198	Find $ a_{ 4 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = \left( -30 \right) $.	9
199	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	9
200	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 3 $.	9