The first term of an A.P. of 30 non-negative terms is 10/3 . If the sum of this A.P. is the cube of its last term, then its common difference is :

Mathematics · Sequence and Series

JEE Main 2026 — 4 April, Morning Shift — Question 30

The first term of an A.P. of $30$ non-negative terms is $\frac{10}{3}$ . If the sum of this A.P. is the cube of its last term, then its common difference is :

Option A:
$\frac{5}{87}$
Correct
Option B:
$\frac{25}{83}$
Option C:
$\frac{15}{29}$
Option D:
$\frac{5}{29}$

Answer: A

Step-by-step solution

$\mathrm{a}=\frac{10}{3}: \mathrm{S}_{30}=\left(\mathrm{T}_{30}\right)^{3}$ $\frac{30}{2}\left[2 \times \frac{10}{3}+29 \mathrm{~d}\right]=\left[\frac{10}{3}+29 \mathrm{~d}\right]^{3}$ $15\left(\frac{20}{3}+29 \mathrm{~d}\right)=\left(\frac{10}{3}+29 \mathrm{~d}\right)^{3}$ $15\left(\frac{10}{3}+\frac{10}{3}+29 \mathrm{~d}\right)=\left(\frac{10}{3}+29 \mathrm{~d}\right)^{3}$ By observation $\frac{10}{3}+29 \mathrm{~d}=5$ $29 d=5-\frac{10}{3}=\frac{5}{3}$ $\mathrm{d}=\frac{5}{87}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 4 April, Morning Shift
Subject: Mathematics
Chapter: Sequence and Series
Topic: Arithmetic Progression