Progression Questions for CAT

If $\log a, \log b, \log c$ are in A.P., then the GM of $a$ and $c$ is

Answer the questions independently of each other.

If x + 1, x + a and x + 11 are in GP, where x and a both are positive integers, what is the value of a?

The sum of first 50 natural numbers is:

What is the sum of the first 17 terms of an arithmetic progression if the 3rd term is 6 and the 8th term is 16?

If the sum of three consecutive terms in an AP is 27 and their product is 504, find the terms.

The sum of the first 62 terms of an AP equals the sum of the first 118 terms. The sum of the first 80 terms is how many times the sum of the first 100 terms?

If $a_1 + a_2 + a_3 + \dots + a_n = 4(5^{n+1} - 5),$ then find the value of $a_{6}.$

The sum of the series $\frac{1}{1 \times 5}+\frac{1}{5 \times 9}+\frac{1}{9 \times 13} \ldots+\frac{1}{221 \times 225}$ is

Find the sum of all integers of 3 digits that are divisible by 11.

The sum of the first 12 terms of a GP equals the sum of the first 14 terms. Given that the sum of the first 17 terms is 92, what is the third term of the GP?

Find the sum of the following series: $1 + 4 + 13 + 40 + 121 + \cdots$ up to 10 terms.

What is the maximum sum of the terms in the arithmetic progression 25, $24\; \frac{1}{2}$, 24, ... ?

A student summed consecutive odd numbers starting from 1 and got a total of 666. She realized that a number has been counted twice. What number is it?

Find the sum to $n$ terms of the series $11 + 103 + 1005 + ...$

The sum of all natural numbers less than 201 which are divisible by either 5 or 6 but not by both is?

Evaluate the infinite series:

$S=\sum_{n=1}^{\infty} \left[\left(\frac{1}{4}\right)^n - \left(\frac{1}{6}\right)^n\right]^2.$

Let $d_1, d_2, \dots$ be integers with $d_1 - d_2 + d_3 - d_4 + \dots + (-1)^{n-1}d_n = n^2$ for $n\geq 1$. Find $d_{11} + d_{12} + \dots + d_{201}$.

Find the largest value of $t$ such that $x^t + 1$ divides $1 + x + x^2 + \cdots + x^{143}$.

One side of a staircase is to be closed in by rectangular planks from the floor to each step. The width of each plank is 9 inches and their heights are successively 6 inches, 12 inches, 18 inches and so on. There are 24 planks required in total. Find the area in square feet.