JEE Main 2022MathematicsSequences and SeriesHardNumerical

JEE Main 2022 — Sequences and Series Question with Solution

JEE Main 2022 (29 Jul Shift 1)

Question

If 12×3×4+13×4×5+14×5×6+…+
1100×101×102=k101, then 34k is equal to _______.

Enter your answer

Show full solutionCorrect answer: 286
Correct answer
286

Step-by-step explanation

Given,

12.3.4+13.4.5+….+1100.101.102=k101

⇒22.3.4+23.4.5+….+2100.101.102=2k101

⇒4-22.3.4+5-33.4.5+…..+102-100100.101.102=2k101

⇒12×3-13×4+13×4-14×5+….+1100×101-1101×102=2k101

⇒12×3-1101×102=2k101

⇒1012×3-101101×102=2k

⇒2k=1016-1102

⇒34k=286

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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.