Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

JEE Main 20265 AprilEvening Shift

Exam: JEE Main
Year: 2026
Date: 5 April
Shift: Evening Shift
Subject: Mathematics
Chapter: Sequences and Series

JEE Main 2026 · 5 April · Evening Shift · Mathematics · Sequences and Series

Let A_1, A_2, A_3, , A_ 39 be 39 arithmetic means between the...

Let

A_1, A_2, A_3, \ldots, A_{39}

be

39

arithmetic means between the numbers

59

and

159

. Then the mean of

A_{25}, A_{28}, A_{31}

and

A_{36}

is equal to :

Options

A $129$
B $136$
C $131.50$
D $134$

Correct answer

D. $134$

Step-by-step solution

The sequence

59, A_1, A_2, \ldots, A_{39}, 159

forms an arithmetic progression with

41

terms.

The common difference

d

is given by

d = \dfrac{159 - 59}{39 + 1} = \dfrac{100}{40} = 2.5

The

k

-th arithmetic mean is

A_k = 59 + k \cdot d

The required mean is

\dfrac{A_{25} + A_{28} + A_{31} + A_{36}}{4}

\dfrac{A_{25} + A_{28} + A_{31} + A_{36}}{4} = \dfrac{(59 + 25d) + (59 + 28d) + (59 + 31d) + (59 + 36d)}{4}

= \dfrac{4 \times 59 + 120d}{4} = 59 + 30d

Substituting

d = 2.5

:

= 59 + 30(2.5) = 59 + 75 = 134

Answer:

134

Practice Sequences and Series on Quantrex Academy →

More from Sequences and Series

Let α = 3+4+8+9+13+14+… upto 40 terms. If ( β)^ (α)/(1020) is a root of the equation… JEE Main 2026 The sum 1 + (1)/(2)(1^2 + 2^2) + (1)/(3)(1^2 + 2^2 + 3^2) + … upto 10 terms is equal to : JEE Main 2026 The value of 1^3 - 2^3 + 3^3 - … + 15^3 is: JEE Main 2026 The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms of a… JEE Main 2026 For the functions f(θ) = α ^2θ + β ^2θ , and g(θ) = α ^2θ + β ^2θ , α > β > 0 , let _ 0 <… JEE Main 2026 If the sum of the first 10 terms of the series (1)/(1 + 1^4 × 4) + (2)/(1 + 2^4 × 4) +… JEE Main 2026 Let the sum of the first n terms of an A.P. be 3n^2 + 5n . Then the sum of squares of the… JEE Main 2026 ∑_ n=1 ^ 10 ( (528)/(n(n+1)(n+2)) ) is equal to: JEE Main 2026 Let α=(1)/(4)+(1)/(8)+(1)/(16)+…∞ and β=(1)/(3)+(1)/(9)+(1)/(27)+…∞ . Then the value of… JEE Main 2026 The first term of an A.P. of 30 non-negative terms is (10)/(3) . If the sum of this A.P.… JEE Main 2026 Let a_1, a_2, a_3, … be an A.P. and g_1 = a_1, g_2, g_3, … be an increasing G.P. If a_1 =… JEE Main 2026 The sum (1^3)/(1) + (1^3 + 2^3)/(1 + 3) + (1^3 + 2^3 + 3^3)/(1 + 3 + 5) + ⋯ up to 8… JEE Main 2026 Let α, α + 2, α ∈ ℤ , be the roots of the quadratic equation x(x+2) + (x+1)(x+3) +… JEE Main 2026 Let A be the set of first 101 terms of an A.P., whose first term is 1 and the common… JEE Main 2026 If ∑_ k=1 ^ n a_k = 6n^3 , then ∑_ k=1 ^ 6 ( a_ k+1 - a_k 36 )^2 is equal to _______. JEE Main 2026 Let the arithmetic mean of 1 a and 1 ~b be (5)/(16), a>2 . If α is such that a, 4, α, ~b… JEE Main 2026 Full Sequences and Series list Sequences and Series JEE Maths PYQs JEE Mathematics PYQs All JEE Main PYQs