JEE Main 2019MathematicsSequences and SeriesMediumMCQ

JEE Main 2019 — Sequences and Series Question with Solution

JEE Main 2019 (09 Jan Shift 1)

Question

Let a1, a2, …, a30 be an A.P., S= ∑i=130ai and T= ∑i=115a(2i-1). If a5=27 and S-2T=75, then a10 is equal to:

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Show full solutionCorrect option: A
Correct answer
A52

Step-by-step explanation

Let common difference =d

∴S= ∑i=130ai=3022a1+29 d

∴S=15 2a1+29 d ........ (i)

T=1522a1+14 . 2d

T=15 a1+14d ...........(ii)

a1+4d=27 ......... (iii)

S-2T=75

⇒152a1+29 d-30 a1+14d =75
⇒15 d29-28= 75
⇒d=5
∴  from (iii) a1=7
∴ a10=a1+9d=7+45=52

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About this question

This is a previous-year question from JEE Main 2019, 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.