QJEEM20Ma61d5: JEE Main 2020 Mathematics - Class 11 JEEM20Ma61d5 Solution: Let a n be the n th term of a G.P. of positive terms. and ,…

$\sum\limits_{n = 1}^{100} {{a_{2n + 1}} = 200}$

$\Rightarrow$ a₃ + a₅ + a₇ + .... + a₂₀₁ = 200

$\Rightarrow$ $a{r^2}{{\left( {{r^{200}} - 1} \right)} \over {\left( {{r^2} - 1} \right)}}$ = 200 ....(1)

$\sum\limits_{n = 1}^{100} {{a_{2n}} = 100}$

$\Rightarrow$ a₂ + a₄ + a₆ + ... + a₂₀₀ = 100

$\Rightarrow$ $ar{{\left( {{r^{200}} - 1} \right)} \over {\left( {{r^2} - 1} \right)}}$ = 100 ....(2)

dividing (1) by (2)

we get, r = 2

adding both (1) and (2), we get

a₂ + a₃ + a₄ + a₅ + ..... + a₂₀₁ = 300

$\Rightarrow$ r(a₁ + a₂ + ..... + a₂₀₀) = 300

$\Rightarrow$ a₁ + a₂ + ..... + a₂₀₀ = ${{300} \over r}$

$\Rightarrow$ $\sum\limits_{n = 1}^{200} {{a_n}}$ = ${{300} \over 2}$ = 150