All Questions
Tagged with sequences-and-series arithmetic-progressions
366
questions
9
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Is there a non-trivial arithmetic progression of positive integers such that every number contains the digit $2?$
Let $X:=\{$ positive integers that contain the digit $2\}$
For fixed $m,n\in\mathbb{N},$ define the A.P. $S_{m,n:=}\ \{m,\ m+n,\ m+2n, \ldots\}\ .$
I am interested in $S_{m,n}\cap X,$ and $S_{m,n}\cap ...
- 20.7k
1
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1
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How to form an AP which contains common terms of two other APs?
I got this question when I was going through a question from the infamous entrance exam JEE. It was a question from the JEE Advanced 2018, Paper 1.
The question is as follows:
Let X be the set ...
1
vote
1
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Application of $a_n$ = $S_n$ - $S_{n-1}$ for an arithmetic progression.
Consider the following question:
Let $V_r$ denote the sum of the first r terms of an Arithmetic Progression whose first term is r and common difference is (2r-1). Let $T_r$ = $V_{r+1}$ - $V_r$ -2. ...
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$\frac{a}{x},\frac{b}{y},\frac{c}{z}$ are in HP
If non-zero numbers $a,b,c,x,y$ and $z$ are such that $a,b,c$ are in AP, $x,y,z$ are in GP and $\frac{a}{x},\frac{b}{y},\frac{c}{z}$ are in HP then prove $|a|=|c|$.
I have been trying to solve this ...
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3
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2
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Prove $p,q,r$ are AP if $p\left(\frac{1}{q}+ \frac{1}{r}\right), q\left(\frac{1}{r}+ \frac{1}{p}\right), r\left(\frac{1}{p}+ \frac{1}{q}\right)$ is AP
How should one approach this question. The following is my attempt:
I started by forming the following equation, which is the inherent property of Arithmetic Progression:
$$2 \cdot q\left(\frac{1}{r}+ ...
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votes
4
answers
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Relationship between the squares of first n natural numbers and first n natural odd numbers.
Here's a question from high school mathematics.
If $ 1^2 + 2^2 + 3^2 + 4^2 + 5^2 + \dots + 100^2 = x $, then
($1^2 + 3^2 + 5^2 + \dots + 99^2$) is equal to ?
Options were:
(a) $\frac{x}{2}-2525$
(b) ...
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2
answers
52
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I have got stucked with this concept of A.P.
Q) How to prove that the sequence:$ 2,4,6,8,...,1000$ is an A.P.$($$Arithmetic$ $Progression$)?
First of all, the $1^{st}$ term of this sequence is $2$ and the common difference of this sequence is ...
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0
votes
0
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Formula for calculating the sum of the equation: $y = \lfloor 400(x-6)^{1.1} \rfloor$
I have an equation of $y = \lfloor 400(x-6)^{1.1} \rfloor$ where x is equal to or greater than 6 and increases by an increment of 1.
I want to calculate what the sum of the equations added up together ...
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-2
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2
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What is the formula for finding the summation of the sequence : $1,2,5,12,26,51,...$ upto $n$ terms? [duplicate]
Q)What is the formula for finding the summation of the sequence $1,2,5,12,26,51,...$ upto $n$ terms ?
I know how to find the summation of sequences like $1,2,3,...,$ upto $n$ terms ; $1,2,4,8,...,$ ...
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0
votes
3
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General term for increasing AP's
Can some give an easy general method to find general term of sequences whose difference is in AP?
Example: 1,4,8,13,19....
The difference is 3,4,5... which is in AP.
Through vigorous testing and ...
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1
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0
answers
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If for any element's neighbors' average equals to element in sequence, it is an arithmetic progression
I need to prove that if a sequence $\{a_n\}_{n\in\Bbb N}$ is such that
$$
a_n = \frac{a_{n-1}+a_{n+1}}{2} \quad\forall n\in\Bbb N
$$
then the sequence is arithmetic progression.
I transformed that ...
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2
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1
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given that $a_n$ is an arithmetic sequence, and $a_{14}^2+a_{15}^2+a_{16}^2=35$, $a_{15} > 0$ find the general term of an $a_n$
I am right now in the Hebrew University Academic Prep School which in its level is equivalent to an American high school/college. It's a one-year academic prep school for engineering and exact science....
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Shifted start arithmetic progression formula why it works? $a_n=a_k+(n-k)\cdot d$
Question:The number of zeros in $(10^{60}+1)^2$ is?
The number of zeros in $(10^1+1)^2$ is zero.
The number of zeros in $(10^2+1)^2$ is two.
The number of zeros in $(10^3+1)^2$ is four.
There's a ...
user1285659
0
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Why is $\sum_{k=1}^n {ka_k} = \frac{n(n+1)}{2}\frac{(a_1+2a_n)}{3}$ where $(a_n)$ is an arithmetic progression. [closed]
This is a question about the sum of an arithmetic sequence. Please forgive my lack of experience with LaTex.
To find the sum as asked, I wrote a general term for the arithmetic sequence and used the ...
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1
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Assuming all the terms of A.P. $[a_{n}]$ are integers with $a_{1}=2019$. Find number of such sequence satisfying given condition
Assuming all the terms of A.P. $[a_{n}]$ are integers with $a_{1}=2019$ and for $n\in I^+$ there always exsits positive integer $m$ such that $a_{1}+a_{2}+.....+a_{n}=a_{m}$, then find number of such ...
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