Question

Find an arithmetic progression for which $\begin{cases}S_n-a_1=48\\S_n-a_n=36\\S_n-a_1-a_2-a_{n-1}-a_n=21\end{cases}$

score 104 · Answer 1 · 2021-06-23 18:07:27

104

Views

Find an arithmetic progression for which $\begin{cases}S_n-a_1=48\\S_n-a_n=36\\S_n-a_1-a_2-a_{n-1}-a_n=21\end{cases}$

Published on 23 Jun 2021 - 18:07

score 870 · Answer 2 · 2026-03-27 19:33:42

870

Views

Sum of the series of numbers consisting of AP and GP both.

Published on 27 Mar 2026 - 19:33

score 46 · Answer 3 · 2021-06-29 08:57:30

46

Views

Is there a generalisation possible for arithmetic progression with dynamic cyclic difference?

Published on 29 Jun 2021 - 8:57

score 44 · Answer 4 · 2026-03-27 19:31:59

44

Views

Generalized Arithmetico-Geometic series with a possible application

Published on 27 Mar 2026 - 19:31

score 242 · Answer 5 · 2021-07-12 14:19:20

242

Views

Every quadratic equation of form $px^2 + qx + c = 0$ represents a sum of some arithmetic progression?

Published on 12 Jul 2021 - 14:19

score 280 · Answer 6 · 2021-07-13 10:10:34

280

Views

Sum of all $n$ arithmetic means is equal to $n$ times single arithmetic mean.

Published on 13 Jul 2021 - 10:10

score 95 · Answer 7 · 2021-07-16 18:38:09

95

Views

Is a strictly increasing necessarily a subsequent of an arithmetic progression?

Published on 16 Jul 2021 - 18:38

score 114 · Answer 8 · 2026-03-29 05:58:40

114

Views

Find the sum of the first $50$ terms of the series $a_{n} = -4a_{n-1} + 3$.

Published on 29 Mar 2026 - 5:58

score 27 · Answer 9 · 2021-08-06 16:00:27

27

Views

Solution Verfication on a problem regarding progressions

Published on 06 Aug 2021 - 16:00

score 102 · Answer 10 · 2021-08-06 20:19:41

102

Views

Arbitrarily large arithmetic progressions in the random set of values of a non-lacunary sequence.

Published on 06 Aug 2021 - 20:19

score 104 · Answer 11 · 2021-08-16 07:52:46

104

Views

Let $a_{1}, a_{2}, a_{3}, \dots,a_{n}$ be in ap. given $\sum\limits_{r=1}^\mathbb{10}a_{r}^2 = 1185.$ Find max value of $n $ for $S(n)\ge S(n-1)$

Published on 16 Aug 2021 - 7:52

score 92 · Answer 12 · 2021-08-18 04:38:53

92

Views

Given $7$ distinct positive integers, form an AP with $3$ or $4$ of them

Published on 18 Aug 2021 - 4:38

score 182 · Answer 13 · 2021-09-05 08:32:51

182

Views

Could a nice principe, or at least a simpler alternative proof, be found regarding a lemma of Gauss

Published on 05 Sep 2021 - 8:32

score 92 · Answer 14 · 2026-03-27 19:30:23

92

Views

What is the solution to this problem (Geometric and Arithmetic progression)?

Published on 27 Mar 2026 - 19:30

score 30 · Answer 15 · 2021-09-10 09:54:46

30

Views

Why difference is different between terms of an arithmetic progression?

Published on 10 Sep 2021 - 9:54

List Question

Find an arithmetic progression for which $\begin{cases}S_n-a_1=48\\S_n-a_n=36\\S_n-a_1-a_2-a_{n-1}-a_n=21\end{cases}$

Sum of the series of numbers consisting of AP and GP both.

Is there a generalisation possible for arithmetic progression with dynamic cyclic difference?

Generalized Arithmetico-Geometic series with a possible application

Every quadratic equation of form $px^2 + qx + c = 0$ represents a sum of some arithmetic progression?

Sum of all $n$ arithmetic means is equal to $n$ times single arithmetic mean.

Is a strictly increasing necessarily a subsequent of an arithmetic progression?

Find the sum of the first $50$ terms of the series $a_{n} = -4a_{n-1} + 3$.

Solution Verfication on a problem regarding progressions

Arbitrarily large arithmetic progressions in the random set of values of a non-lacunary sequence.

Let $a_{1}, a_{2}, a_{3}, \dots,a_{n}$ be in ap. given $\sum\limits_{r=1}^\mathbb{10}a_{r}^2 = 1185.$ Find max value of $n $ for $S(n)\ge S(n-1)$

Given $7$ distinct positive integers, form an AP with $3$ or $4$ of them

Could a nice principe, or at least a simpler alternative proof, be found regarding a lemma of Gauss

What is the solution to this problem (Geometric and Arithmetic progression)?

Why difference is different between terms of an arithmetic progression?

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