Question

if 2+2^2+2^3+...........+n terms is 1025 then the value of n is
PLEASE ANSWER FAST ​

Answer 1

2, 2², 2³, ...

form a G.P.

with first term (a) = 2.

and common ratio (r) = 2

now, for this G.P.

$S_{n} = a(\frac{{r}^{n} - 1}{r - 1}) = 1022 \\</p><p>1022 = 2(\frac{{2}^{n} - 1}{2 - 1})$

511 = 2ⁿ - 1

2ⁿ = 512

2ⁿ = ${2}^{9}$

n = 9