# Recent questions tagged arithmetic-progression

1

Three positive integers $x,y$ and $z$ are in arithmetic progression. If $y – x 2$ and $xyz = 5(x+y+z),$ then $z-x$ equals$12$$8$$14$$10$

2

If $(2n+1)+(2n+3)+(2n+5)+\dots+(2n+47)=5280,$ then what is the value of $1+2+3+\dots+n$ _______

3

The number of common terms in the two sequences: $15, 19, 23, 27,\dots,415$ and $14, 19, 24, 29,\dots,464$ is$18$$19$$21$$20$

4

The value of the sum $7 \times 11 + 11 \times 15 + 15 \times 19 + \dots$ + $95 \times 99$ is$80707$$80773$$80730$$80751$

5

Let $a_{1},a_{2},\dots , a_{52}$ be a positive integers such that $a_{1}<a_{2}<\dots < a_{52}$. Suppose, their arithmetic mean is one less than the arithmetic mean of $a...

6

Let $x, y, z$ be three positive real numbers in a geometric progression such that $x < y < z$. If $5x$, $16y$, and $12z$ are in an arithmetic progression then the common ...

7

If $\log\left ( 2^{a} \times 3^{b}\times 5^{c}\right )$ is the arithmetic mean of $\log\left ( 2^{2} \times 3^{3}\times 5 \right ),$ $\log\left ( 2^{6} \times3\times 5^{7...

8

If the square of the $7^{\text{th}}$ term of an arithmetic progression with positive common difference equals the products of the $3^{\text{rd}}$ and $17^{\text{th}}$ ter...

9

Let $a_{1}, a_{2},\ldots, a_{3n}$ be an arithmetic progression with $a_{1} = 3$ and $a_{2}=7$. If $a_{1}+ a_{2}+\ldots +a_{3n}=1830$, then what is the smallest positive...

10

A series $\text{S1}$ of five positive integers is such that the third term is half the first term and the fifth term is $20$ more than the first term. In series $\text{S2...

11

12

Fourth term of an arithmetic progression is $8$. What is the sum of the first $7$ terms of the arithmetic progression?$7$$64$$56$Cannot be determined

13

Consider the set $\text{S} = \left \{ 1, 2, 3, \dots,1000 \right \}$. How many arithmetic progressions can be formed from the elements of $\text{S}$ that start with $1$ a...

14

If $a_{1},a_{2}\dots$ are in A.P., then, $\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\dots+\frac{1}{\sqrt{a_{n}}+\sqrt{a_{n+1}}}$ is equal to...

15

if $\log_3\left(2^x - 5\right), \: \log_3\left(2^x - \frac{7}{2}\right)$ are in arithmetic progression, then the value of $x$ is equal to$5$$4$$2$$3$

16

The sum of $3$-rd and $15$-th elements of an arithmetic progression is equal to the sum of $6$-th, $11$-th and $13$-th elements of the same progression. Then which elemen...

17

If the sum of first $11$ terms of an arithmetic progression equals that of a first $19$ terms, then what is the sum of the first $30$ terms?$0$$-1$$1$Not unique

18

Consider the set $\text{S} = \{1, 2, 3, \dots, 1000\}.$ How many arithmetic progressions can be formed from the elements of $\text{S}$ that start with $1$ and with $1000$...