Sequences and Series

JEE Main 2025 (Online) 22nd January Morning ShiftMCQMedium📈 Topic in 37% papers+4−1

Ques. 1JEE Main 2025, 22 January (Morning Shift)

Let a1,a2,a3, be a G.P. of increasing positive terms. If a1a5=28 and a2+a4=29, then a6 is equal to:

Answer

(2) 784

Solution

In a G.P. a1a5=a2a4=a32, so a2a4=28 and a2+a4=29.

a2, a4 are the roots of x2-29x+28=0: 1 and 28 (increasing G.P.)

a2=1, a4=28, r2=28

a6=a4r2=28 28=784

Answer: (2)

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Ques. 2JEE Main 2025, 22 January (Morning Shift)

If r=1nTr= (2n-1)(2n+1)(2n+3)(2n+5)64, then n r=1n ( 1Tr ) is equal to :

Ques. 3JEE Main 2025, 22 January (Evening Shift)

Suppose that the number of terms in an A.P. is 2k, k . If the sum of all odd terms of the A.P. is 40, the sum of all even terms is 55 and the last term of the A.P. exceeds the first term by 27, then k is equal to:

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