CAT 2025 Progression Question (Hard)

Question

In the set of consecutive odd numbers 1,3,5, ldots, 57 , there is a number k such that the sum of all the elements less than k is equal to the sum of all the elements greater than k . Then, k equals

Accepted Answer

The sum of all the elements in the given set Sum of first 29 odd numbers 29 2 841 Let s assume that k is the m_ th term. Sum of terms less than k sum of first m-1 odd numbers m-1 2 841-m 2 m-1 2 841 - m 2 m 2 - 2m 1 840 - 2m 2 2m 0 m 2 - m - 420 0 m - 21 m 20 0 m 21 -20 m 20. And the 20th term is 2

CAT 2025

Quantitative

Progression

Hard

$In the set of consecutive odd numbers ({1,3,5, \ldots, 57}), there is a number (k) such that the sum of all the elements less than (k) is equal to the sum of all the elements greater than (k). Then, (k) equals$

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