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
301	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 6 $.	8
302	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = 10 $.	8
303	Find $ a_{ 15 } $ of an arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 4 $.	8
304	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 2 $.	8
305	Find $ a_{ 8 } $ of an arithmetic progression if $ a_1 = 3 ~~ \text{and} ~~ d = 3 $.	8
306	Find $ S_{ 98 } $ ( sum of first $ 98 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 7 $.	8
307	Find $ S_{ 18 } $ ( sum of first $ 18 $ terms ) of arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = -9 $.	8
308	Find $ a_{ 0 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 0 $.	8
309	Find $ S_{ 90 } $ ( sum of first $ 90 $ terms ) of arithmetic progression if $ a_1 = 300 ~~ \text{and} ~~ d = 150 $.	8
310	Find $ a_{ 37 } $ of an arithmetic progression if $ a_1 = 262 ~~ \text{and} ~~ d = \left( -5 \right) $.	8
311	Find $ a_1 $ (first term of arithmetic progression) if $ d = 4 ~~ \text{and} ~~ a_{ 5 } = 20 $.	8
312	Find $ a_{ 36 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 7 $.	8
313	Find $ a_{ 50 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $.	8
314	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 462 ~~ \text{and} ~~ d = \left( -9 \right) $.	8
315	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 17 }{ 3 } ~~ \text{and} ~~ d = \frac{ 23 }{ 18 } $.	8
316	Find $ a_{ 93 } $ of an arithmetic progression if $ a_1 = -11 ~~ \text{and} ~~ d = 4 $.	8
317	$$ a_{ 2 } = 20 ~~,~~ S_{ 2 } = 18 ~~,~~ a_1 = ? ~~,~~ d = ? $$	8
318	Find $ a_{ 58 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 3 $.	8
319	Find $ a_{ 66 } $ of an arithmetic progression if $ a_1 = 55 ~~ \text{and} ~~ d = 122 $.	8
320	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 3 $.	8
321	Find $ a_{ 77 } $ of an arithmetic progression if $ a_1 = 8 ~~ \text{and} ~~ d = 18 $.	8
322	Find $ a_{ 22 } $ of an arithmetic progression if $ a_1 = 58 ~~ \text{and} ~~ d = 23 $.	8
323	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	8
324	Find $ a_{ 100 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $.	8
325	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 16 ~~ \text{and} ~~ d = 32 $.	8
326	Find $ S_{ 14 } $ ( sum of first $ 14 $ terms ) of arithmetic progression if $ a_1 = 42 ~~ \text{and} ~~ d = -5 $.	8
327	Find $ S_{ 64 } $ ( sum of first $ 64 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	8
328	Find $ a_{ 85 } $ of an arithmetic progression if $ a_1 = -25 ~~ \text{and} ~~ d = \left( -12 \right) $.	8
329	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	8
330	Find $ a_{ 52 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	8
331	Find $ a_{ 7 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	8
332	Find $ S_{ 20 } $ ( sum of first $ 20 $ terms ) of arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = 4 $.	8
333	Find $ S_{ 10 } $ ( sum of first $ 10 $ terms ) of arithmetic progression if $ a_1 = 6 ~~ \text{and} ~~ d = 1 $.	8
334	$$ a_{ 12 } = -15 ~~,~~ S_{ 12 } = -109 ~~,~~ a_1 = ? ~~,~~ d = ? $$	8
335	Find $ a_{ 6 } $ of an arithmetic progression if $ a_1 = 330 ~~ \text{and} ~~ d = \left( -90 \right) $.	8
336	Find $ a_{ 91 } $ of an arithmetic progression if $ a_1 = 5 ~~ \text{and} ~~ d = \left( -19 \right) $.	8
337	$$ a_1 = 15 ~,~ d = 10 ~,~ S_n = 400 ~,~ n = ? $$	8
338	Find $ a_{ 12 } $ of an arithmetic progression if $ a_1 = \frac{ 3 }{ 2 } ~~ \text{and} ~~ d = \frac{ 3 }{ 4 } $.	8
339	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	8
340	Find $ a_{ 60 } $ of an arithmetic progression if $ a_1 = -29 ~~ \text{and} ~~ d = \left( -20 \right) $.	8
341	Find $ S_{ 100 } $ ( sum of first $ 100 $ terms ) of arithmetic progression if $ a_1 = -5 ~~ \text{and} ~~ d = 3 $.	8
342	Find $ S_{ 70 } $ ( sum of first $ 70 $ terms ) of arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = 1 $.	8
343	Find $ S_{ 15 } $ ( sum of first $ 15 $ terms ) of arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $.	7
344	Find $ a_{ 30 } $ of an arithmetic progression if $ a_1 = 10 ~~ \text{and} ~~ d = \left( -3 \right) $.	7
345	Find $ S_{ 48 } $ ( sum of first $ 48 $ terms ) of arithmetic progression if $ a_1 = 2 ~~ \text{and} ~~ d = 2 $.	7
346	Find $ a_{ 9 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 5 $.	7
347	Find $ a_{ 20 } $ of an arithmetic progression if $ a_1 = 4 ~~ \text{and} ~~ d = 2 $.	7
348	Find $ a_{ 33 } $ of an arithmetic progression if $ a_1 = -12 ~~ \text{and} ~~ d = \left( -11 \right) $.	7
349	Find $ a_{ 5 } $ of an arithmetic progression if $ a_1 = 1 ~~ \text{and} ~~ d = \left( -4 \right) $.	7
350	Find $ a_{ 43 } $ of an arithmetic progression if $ a_1 = 11 ~~ \text{and} ~~ d = 9 $.	7