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
251	Find $ a_{ 96 } $ of an arithmetic progression if $ a_1 = -30 ~~ \text{and} ~~ d = \left( -2 \right) $.	9
252	Find $ a_{ 84 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 20 $.	9
253	Find $ a_{ 76 } $ of an arithmetic progression if $ a_1 = 17 ~~ \text{and} ~~ d = 2 $.	9
254	Find $ a_{ 58 } $ of an arithmetic progression if $ a_1 = -28 ~~ \text{and} ~~ d = 15 $.	9
255	Find $ a_{ 109 } $ of an arithmetic progression if $ a_1 = 963 ~~ \text{and} ~~ d = \left( -27 \right) $.	9
256	Find $ a_{ 97 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = \left( -18 \right) $.	8
257	Find $ a_{ 93 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = \left( -10 \right) $.	8
258	Find $ a_{ 97 } $ of an arithmetic progression if $ a_1 = -16 ~~ \text{and} ~~ d = 18 $.	8
259	Find $ a_{ 17 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	8
260	Find $ S_{ 50 } $ ( sum of first $ 50 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	8
261	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 3 $.	8
262	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = \left( -4 \right) $.	8
263	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 4 $.	8
264	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $.	8
265	Find $ a_{ 24 } $ of an arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 6 $.	8
266	Find $ a_{ 41 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 0 $.	8
267	Find $ S_{ 200 } $ ( sum of first $ 200 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $.	8
268	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 7 $.	8
269	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 5 $.	8
270	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 12 $.	8
271	Find $ a_{ 73 } $ of an arithmetic progression if $ a_1 = 18 ~~ \text{and} ~~ d = 12 $.	8
272	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 7 ~~ \text{and} ~~ d = 2 $.	8
273	$$ a_1 = 19 ~,~ a_n = 118 ~,~ S_n = 822 ~,~ n = ? $$	8
274	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = \left( -5 \right) $.	8
275	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 9 ~~ \text{and} ~~ d = 4 $.	8
276	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 0 $.	8
277	Find $ a_{ 29 } $ of an arithmetic progression if $ a_1 = -24 ~~ \text{and} ~~ d = 8 $.	8
278	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 4 $.	8
279	Find $ a_{ 1000 } $ of an arithmetic progression if $ a_1 = -2 ~~ \text{and} ~~ d = 10 $.	8
280	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $.	8
281	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	8
282	Find $ a_{ 10 } $ of an arithmetic progression if $ a_1 = \frac{ 23 }{ 100 } ~~ \text{and} ~~ d = \frac{ 1 }{ 10 } $.	8
283	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = -3 $.	8
284	Find $ a_{ 89 } $ of an arithmetic progression if $ a_1 = 25 ~~ \text{and} ~~ d = 10 $.	8
285	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = -9 ~~ \text{and} ~~ d = -3 $.	8
286	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 8 $.	8
287	Find $ a_{ 57 } $ of an arithmetic progression if $ a_1 = 13 ~~ \text{and} ~~ d = \left( -5 \right) $.	8
288	Find $ a_{ 13 } $ of an arithmetic progression if $ a_1 = 31 ~~ \text{and} ~~ d = 10 $.	8
289	Find $ S_{ 13 } $ ( sum of first $ 13 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 10 $.	8
290	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = 28 ~~ \text{and} ~~ d = 9 $.	8
291	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 12 ~~ \text{and} ~~ d = 4 $.	8
292	Find $ S_{ 12 } $ ( sum of first $ 12 $ terms ) of arithmetic progression if $ a_1 = -29 ~~ \text{and} ~~ d = -7 $.	8
293	Find $ a_{ 36 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 6 $.	8
294	$$ a_1 = 5 ~,~ d = 7 ~,~ S_n = 365 ~,~ n = ? $$	8
295	Find $ a_{ 46 } $ of an arithmetic progression if $ a_1 = 206 ~~ \text{and} ~~ d = \left( -4 \right) $.	8
296	Find $ S_{ 6 } $ ( sum of first $ 6 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 2 $.	8
297	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	8
298	Find $ S_{ 70 } $ ( sum of first $ 70 $ terms ) of arithmetic progression if $ a_1 = 100 ~~ \text{and} ~~ d = 100 $.	8
299	Find $ a_{ 62 } $ of an arithmetic progression if $ a_1 = -27 ~~ \text{and} ~~ d = 6 $.	8
300	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 4 $.	8