JEE Main 2022MathematicsSequences And SeriesArithmetic ProgressionmediumNumerical

JEE Main 2022 — Sequences And Series Question with Solution

From: JEE Main 2022 (Online) 28th June Morning Shift

Question

Let A = {1, a1, a2 ....... a18, 77} be a set of integers with 1 < a1 < a2 < ....... < a18 < 77.

Let the set A + A = {x + y : x, y A} contain exactly 39 elements. Then, the value of a1 + a2 + ...... + a18 is equal to _____________.

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Show full solutionCorrect answer: 702
Correct answer
702

Step-by-step explanation

If we write the elements of , we can certainly find 39 distinct elements as .

It means all other sums are already present in these 39 values, which is only possible in case when all numbers are in A.P.

Let the common difference be ''.



So,

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About this question

This is a previous-year question from JEE Main 2022, covering the Sequences And Series chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.