JEE Main 2026 · 2 Apr · Shift 2 · Mathematics Q4

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MathematicsSingle correct+4 / -1Question 4 of 75

Let $a_1,a_2,a_3,\dots$ be an A.P. and $g_1=a_1,g_2,g_3,\dots$ be an increasing G.P. If $a_1=a_2+g_2=1$ and $a_3+g_3=4$ , then $a_{10}+g_5$ is equal to :

Answer and worked solution

Official answer: D

Unknowns. $a_1=g_1=1$ ; let $d$ be the common difference and $r$ the common ratio.

Conditions. $a_2+g_2=1+d+r=1$ , so $d=-r$ . $a_3+g_3=1+2d+r^2=4$ , so $r^2-2r-3=0$ ; increasing G.P. means $r=3$ , $d=-3$ .

Value. $a_{10}+g_5=(1-27)+81=55$ .

(D)

Topics:Geometric progression Arithmetic progression

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JEE Main 2026 · 2 Apr · Shift 2, Mathematics question 4