List of top Mathematics Questions on Arithmetic Progression

The common difference of the A.P.: $ a_1, a_2, \ldots, a_m $ is 13 more than the common difference of the A.P.: $ b_1, b_2, \ldots, b_n $. If $ b_{31} = -277 $, $ b_{43} = -385 $ and $ a_{78} = 327 $, then $ a_1 $ is equal to:

Let $a_1,a_2,a_3,a_4$ be an A.P. of four terms such that each term of the A.P. and its common difference are integers. If $a_1+a_2+a_3+a_4=48$ and $a_1^2a_2a_3a_4+1^4=361$, then the largest term of the A.P. is equal to

Consider an A.P. $a_1,a_2,\ldots,a_n$; $a_1>0$. If $a_2-a_1=-\dfrac{3}{4}$, $a_n=\dfrac{1}{4}a_1$, and \[ \sum_{i=1}^{n} a_i=\frac{525}{2}, \] then $\sum_{i=1}^{17} a_i$ is equal to

The vertices B and C of a triangle ABC lie on the line $ \frac{x}{1} = \frac{1-y}{2} = \frac{z-2}{3} $. The coordinates of A and B are (1, 6, 3) and (4, 9, 6) respectively and C is at a distance of 10 units from B. The area (in sq. units) of $ \triangle ABC $ is:

If the sum of the first four terms of an A.P. is $6$ and the sum of its first six terms is $4$, then the sum of its first twelve terms is

The value of x for which $ 2x, (x + 10) $ and $ (3x + 2) $ are the three consecutive terms of an A.P. is :

Which of the following sequence is not an A.P. ?

In an A.P., $a = -3$ and $S_{17} = 357$. The value of $a_{17}$ is

In an A.P., $15^{th}$ term exceeds the $8^{th}$ term by 21. If sum of first 10 terms is 55, then form the A.P.

The sum of first n terms of an A.P. is $2n^{2} + 13n$. Find its $n^{th}$ term and hence $10^{th}$ term.

Which of the following sequence is $\textit{not }$an A.P. ?

The common difference of the AP : $\sqrt{2}, 2\sqrt{2}, 3\sqrt{2}, 4\sqrt{2}, \dots$ is :

In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato. The other potatoes are arranged 3 m apart in a straight line, with a total of 10 potatoes. A competitor starts from the bucket, picks up the nearest potato, runs back to the bucket to drop it in, then returns to pick up the next potato. This process continues until all the potatoes are in the bucket.

(i) What is the distance covered to pick up the first potato and drop it in bucket?
(ii) What is the distance covered to pick up the second potato and drop it in bucket?
(iii) (a) What is the total distance the competitor has to run? OR
(iii) (b) If average speed of competitor is 5 m/s, then find the average time taken by competitor to put all the potatoes in the bucket.}

The common difference of the AP : $\sqrt{2}, 2\sqrt{2}, 3\sqrt{2}, 4\sqrt{2}, \dots$ is :

If $a_n$ represents $n^{\text{th}}$ term of the A.P. $-\frac{15}{4}, -\frac{10}{4}, -\frac{5}{4}, \dots$ then value of $a_{16} - a_{12}$ is

The numbers $x$, $x+4$ and $x+8$ are in A.P. with common difference:

A watermelon vendor arranged the watermelons similar to shown in the adjoining picture. The number of watermelons in subsequent rows differ by 'd'. The bottommost row has 101 watermelons and the topmost row has 1 watermelon. There are 21 rows from bottom to top. Based on the above information, answer the following questions :
(i) Find the value of 'd'.
(ii) How many watermelons will be there in the 15th row from the bottom?
(iii) (a) Find the total number of watermelons from bottom to top. OR
(iii) (b) If the number of watermelons in the nth row from top is equal to
the number of watermelons in the nth row from bottom, find the value of n.

For any natural number n, $6^n$ ends with the digit :

In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato. The other potatoes are arranged 3 m apart in a straight line, with a total of 10 potatoes. A competitor starts from the bucket, picks up the nearest potato, runs back to the bucket to drop it in, then returns to pick up the next potato. This process continues until all the potatoes are in the bucket. Based on the above information, answer the following questions :

Your elder brother wants to buy a car and plans to take a loan from a bank for his car. He repays his total loan of 1,18,000 by paying every month, starting with the first instalment of1,000 and he increases the instalment by 100 every month.

Tejas is standing at the top of a building and observes a car at an angle of depression of 30° as it approaches the base of the building at a uniform speed. 6 seconds later, the angle of depression increases to 60", and at that moment, the car is 25 m away from the building.

Kolam' is a decorative art which is made with rice flour in South Indian States. It is drawn on grid pattern of dots. One such art work is shown below.

Observe the given figure carefully. There are 4 dots in first square, 8 dots in second square, 12 dots in third square and so on. Based on the above, answer the following questions:

Consider an A.P. $a_1,a_2,\ldots,a_n$ with $a_1>0$, $a_2-a_1=-\dfrac{3}{4}$ and $a_n=\dfrac{a_1}{4}$. If \[ \sum_{i=1}^{n} a_i=\frac{525}{2}, \] then find $\sum_{i=1}^{17} a_i$.

Let 4 integers $a_1, a_2, a_3, a_4$ are in A.P. with integral common difference $d$ such that $a_1+a_2+a_3+a_4=48$ and $a_1a_2a_3a_4+d^4=361$. Then the greatest term in this A.P. is

Evaluate \[ \left(\frac{4}{7}+\frac{1}{3}\right)+\left(\frac{4}{7}+\frac{4}{3}\right)\left(\frac{1}{3}\right) +\left(\frac{4}{7}+\frac{4}{3}\right)^2\left(\frac{1}{3}\right)^2+\cdots \]