JEE Main 2022 · 26 Jun · Shift 2 · Mathematics Q27

MathematicsInteger+4 / -1Question 27 of 90

If $a_1\,(>0)$ , $a_2$ , $a_3$ , $a_4$ , $a_5$ are in a G.P., $a_2+a_4=2a_3+1$ and $3a_2+a_3=2a_4$ , then $a_2+a_4+2a_5$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 40

Ratio. $3a_2+a_2r=2a_2r^2$ gives $2r^2-r-3=0$ : $r=\frac32$ or $-1$ . With $r=-1$ the first condition forces $a_1<0$ , so $r=\frac32$ .

Find $a_2$ . $a_2\left(1+\frac94-3\right)=1$ , so $a_2=4$ ; then $a_4=9$ , $a_5=\frac{27}2$ .

Value. $4+9+27=40$ .

Answer: 40

JEE Main 2022 · 26 Jun · Shift 2, Mathematics question 27