Question

Dada a Pg (2, 4 , 8 , 16 ...) , Calcule o valor de n para que a soma dos n primeiros termos seja 4.094

Answer 1

$\boxed{Sn = \dfrac{a_1\cdot(q^n-1)}{q-1}} \\ \\ q = 2 \\ a_1 = 2 \\ Sn = 4094 \\ \\ \\ 4094 = \dfrac{2.(2^n-1)}{2-1} \\ \\ 4094 = 2.(2^n-1) \\ \\ \dfrac{4094}{2} = 2^n - 1 \\ \\ 2047 + 1 = 2^n \\ \\ 2048 = 2^n \\ \\ 2^{11} = 2^n \\ \\ \\ \boxed{n = 11}$