List of top Mathematics Questions on nth Term of an AP

Given that $ n $ number of arithmetic means are inserted between two pairs of numbers $ a,2b $ and $ 2a,b $; where $ a,b \in R $. If the $ m^{th} $ means in the two cases are the same, then the ratio $ a:b $ is equal to

What is the sum of the infinite series $ S = \sum_{n=0}^{\infty} \frac{1}{3^n} $?

Let $a_1, a_2, a_3, \ldots$ be an AP If $a_7=3$, the product $a_1 a_4$ is minimum and the sum of its first $n$ terms is zero, then $n !-4 a_{n(n+2)}$ is equal to :

Let $a,b,c>1,a^3,b^3 \text{ and } c^3$ be in A.P., and $log_ab, log_ca \text{ and } log_bc$ be in G.P. If the sum of first 20 terms of an A.P., whose first term is $\frac{a+4b+c}{3}$ and the common difference is $\frac{a−8b+c}{10}$ is −444, then abc is equal to:

Let $a, b, c>, a^3, b^3$ and $c^3$ be in AP, and $\log _a b, \log _c a$ and $\log _b c$ be in GP If the sum of first 20 terms of an AP, whose first term is $\frac{a+4 b+c}{3}$ and the common difference is $\frac{a-8 b+c}{10}$ is $-444$, then $a b c$ is equal to:

The $8^{\text {th }}$ common term of the series
$S_1=3+7+11+15+19+\ldots \ldots$
$S_2=1+6+11+16+21+\ldots $ is ______

Let $a_1, a_2, \ldots, a_n$ be in AP If $a_5=2 a_7$ and $a_{11}=18$, then $12\left(\frac{1}{\sqrt{a_{10}}+\sqrt{a_{11}}}+\frac{1}{\sqrt{a_{11}}+\sqrt{a_{12}}}+\ldots+\frac{1}{\sqrt{a_{17}}+\sqrt{a_{18}}}\right)$ is equal to

The mean and variance of 7 observations are 8 and 16 respectively If one observation 14 is omitted and $a$ and $b$ are respectively mean and variance of remaining 6 observation, then $a+3 b-5$ is equal to ______

In an A.P., if the 5^th term is $ \frac{1}{7} $ and the 7^th term is $ \frac{1}{5} $, then the sum of the first 35 terms is ______.

A man repays a loan of Rs. 3250 by paying Rs. 20 in the first month and then increases the payment by Rs. 15 every month. The number of months it takes to clear the loan is

A sum of Rs. 280 is to be used to award four prizes. If each prize after the first prize is Rs. 20 less than its preceding prize, then the value of the fourth prize is

Three numbers are in arithmetic progression (A.P.). Their sum is 21 and the product of the first number and the third number is 45. Then the product of these three numbers is:

If $ a+1, 2a+1, 4a-1 $ are in arithmetic progression, then the value of $ a $ is:

The $ 30^{th} $ term of the arithmetic progression $ 10, 7, 4, \dots $ is:

Three numbers $ x, y, $ and $ z $ are in arithmetic progression (A.P.). If $ x+y+z = -3 $ and $ xyz = 8 $, then $ x^2+y^2+z^2 $ is equal to:

In an A.P., the $6^{\text{th}}$ term is $52$ and the $11^{\text{th}}$ term is $112$. Then the common difference is equal to:

Which term of the AP: 121, 117, 113, ..... is its first negative term?

Which term of the AP : 3, 15, 27, 39, ……… will be 132 more than its 54^th term?

The 17^th term of an AP exceeds its 10^th term by 7. Find the common difference.