JEE Main 2022 · 29 Jul · Shift 1 · Mathematics Q24

MathematicsInteger+4 / -1Question 24 of 90

Let $a_1,a_2,a_3,\dots$ be an A.P. If $\displaystyle\sum_{r=1}^\infty\frac{a_r}{2^r}=4$ , then $4a_2$ is equal to _______.

Your answer

Answer and worked solution

Official answer: 16

Sum. With $a_r=a+(r-1)d$ : $\sum\frac a{2^r}=a$ and $\sum\frac{(r-1)d}{2^r}=d$ . So $a+d=a_2=4$ .

Answer: 16

JEE Main 2022 · 29 Jul · Shift 1, Mathematics question 24