CAT 2022 Question Paper | Quant Slot 2

CAT 2022 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 19 : Consider the arithmetic progression \(3,7,11, \ldots\) and let \(A_n\) denote the sum of the first \(n\) terms of this progression. Then the value of \(\frac{1}{25} \sum_{n=1}^{25} A_n\) is

Video Explanation

Explanatory Answer

a = 3
d = 4
Sum of first n terms,
A_n = \( \frac { n } { 2 } ( 2 a + ( n - 1 ) d ) \)
\( \frac { 1 } { 25 } \sum _ { n = 1 } ^ { 25 } A _ { n } = \frac { 1 } { 25 } \sum _ { n = 1 } ^ { 25 } \frac { n } { 2 } ( 2 a + ( n - 1 ) d ) \)
\( = \frac { 1 } { 25 } \sum _ { n = 1 } ^ { 25 } \frac { n } { 2 } ( 6 + ( n - 1 ) 4 ) \)
\( = \frac { 1 } { 25 } \sum _ { n = 1 } ^ { 25 } n ( 2 n + 1 ) \)
\( = \frac { 1 } { 25 } \left( 2 \sum _ { n = 1 } ^ { 25 } n ^ { 2 } + \sum _ { n = 1 } ^ { 25 } n \right) \)
\( = \frac { 1 } { 25 } \left( 2 \times \frac { 25 \times 26 \times 51 } { 6 } + \frac { 25 \times 26 } { 2 } \right) \)
\( = 2 \times 17 \times 13 + 13 \)
\( = 35 \times 13 \)
= 455

The question is " Consider the arithmetic progression \(3,7,11, \ldots\) and let \(A_n\) denote the sum of the first \(n\) terms of this progression. Then the value of \(\frac{1}{25} \sum_{n=1}^{25} A_n\) is "

Hence, the answer is '455'

Choice C is the correct answer.