Question

Quantos termos devemos tomar na PG (3, 6, 12...) para que a soma seja 381

Answer 1

$\\ a1 = 3 \\ q = 2 \\ n = ?$


$\\ Sn = \frac{a1(q^{n}-1) }{q - 1}$

$\\ 381 = \frac{3.(2^{n} - 1 )}{2 - 1}$

$\\ 381 = 3.(2^{n} - 1)$

$\\ 2^{n} - 1 = \frac{381}3}$

$2^{n} - 1 = 127$

$2^{n} = 127 + 1$

$\\ \\ 2^{n} = 128 \\ \\ 2^{n} = 2^{7} \\ \\ n = 7$