List of top Mathematics Questions on Arithmetic Progression asked in JEE Main

If the second, third, and fourth terms in the expansion of $ (x + y)^n $ are $ 135 $, $ 30 $, and $ \frac{10}{3} $, respectively, then $ 6\left(n^3 + x^2 + y\right) $ is equal to ______.

An arithmetic progression is written in the following way

The sum of all the terms of the 10^th row is ______ .

A software company sets up m number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of the second day, 4 more computer systems crashed on the start of the third day and so on, then it took 8 more days to finish the assignment. The value of m is equal to :

Let 3, 7, 11, 15, ...., 403 and 2, 5, 8, 11, . . ., 404 be two arithmetic progressions. Then the sum, of the common terms in them, is equal to _________.

If 2^nd, 8^th, 44^th terms of A.P. are 1^st, 2^nd and 3^rd terms respectively of G.P. and first term of A.P. is 1 then the sum of first 20 terms of A.P. is

Let m and n be the coefficient of $7^{th}$ and $13^{th}$ term in expansion of $\bigg(\frac{1}{3x^{\frac{1}{3}}} +\frac{1}{2x^{\frac{2}{5}}}\bigg)^{18}$, then $\bigg(\frac{m}{n}\bigg)^{\frac{1}{3}}$ is:

In an increasing arithmetic progression $a_1, a_2,..., a_n$ if $a_6 = 2$ and product of $a_1$, $a_5$ and $a_4$ is greatest, then the value of d is equal to

The 20^th term from the end of the progression \[ 20, 19, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, \ldots, -129 \frac{1}{4} \] is:

The sum of the common terms of the following three arithmetic progressions$3,7,11,15, \ldots , 399$, $2,5,8,11, \ldots , 359$and $2,7,12,17, \ldots , 197,$ is equal to _____

Let $A_1, A_2, A_3$ be the three $A P$ with the same common difference $d$ and having their first terms as $A , A +1, A +2$, respectively, Let $a, b, c$ be the $7^{\text {th }}, 9^{\text {th }}, 17^{\text {th }}$ terms of $A_1, A_2, A_3$, respectively such that $\begin{vmatrix}a & 7 & 1 \\ 2 b & 17 & 1 \\ c & 17 & 1\end{vmatrix}+70=0$If $a=29$, then the sum of first 20 terms of an AP whose first term is $c-a-b$ and common difference is $\frac{d}{12}$, is equal to

Find the sum of series: $2*2^2 - 2*3^2 + 2*4^2 +$ $….(20 \,terms)$

3, 8, 13, ......,373 are in arithmetic series. The sum of numbers not divisible by three is

If (21)18 + 20·(21)17 + (20)2 · (21)16 + ……….. (20)18 = k (2119 – 2019) then k =

Let $x_1, x_2, \dots, x_{100}$ be in an arithmetic progression, with $x_1 = 2$ and their mean equal to 200. If $y_i = (i \cdot x_i)$, then the mean of $y_1, y_2, \dots, y_{100}$ is:

If $(20)^{19}$ + $2(21)(20)^{18} + 3(21)^2 (20)^{17} +$ $\cdots + 20(21)^{19} =$ $k(20)^{19}$, then $k$ is equal to _____ :

If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1 : 7 and a + n = 33, then the value of n is:

If
$\sum_{k=1}^{10} \frac{k}{k^4 + k^2 + 1} = \frac{m}{n}$
where m and n are co-prime, then m + n is equal to

Different A.P.’s are constructed with the first term 100, the last term 199, and integral common differences. The sum of the common differences of all such A.P.’s having at least 3 terms and at most 33 terms is ______.

Let a₁, a₂, a₃,…. be an A.P. If
$\begin{array}{l} \displaystyle\sum\limits_{r=1}^\infty\frac{a_r}{2^r}=4,\end{array}$
then 4a₂ is equal to ________.

If $x=∑_{n=0}^∞a^n,y=∑_{n=0}^∞b^n,z=∑_{n=0}^∞c^n$, where a, b, c are in A.P. and |a| < 1, |b| < 1, |c| < 1, abc≠ 0, then :

Let 3, 6, 9, 12, … upto 78 terms and 5, 9, 13, 17, … upto 59 terms be two series. Then, the sum of terms common to both the series is equal to _____.

The series of positive multiples of 3 is divided into sets: {3}, {6, 9, 12}, {15, 18, 21, 24, 27},…… Then the sum of the elements in the 11^th set is equal to ________.