Question

(UEL) Considere a progressão (-3, 1, -1/3, ...). O produto de seus 12 primeiros termos é:

Answer 1

$q=1/(-3) = \dfrac{-1}{3} \\\\ a_{1}=-3 \\\\ P_{n}= a_{1}^n*q^ \dfrac{n(n-1)}{2} \\\\\\ P_{12}= (-3)^{12}*( \frac{-1}{3}) ^ \dfrac{12(12-1)}{2} P_{12}= (-3)^{12}*( \frac{-1}{3}) ^{66} \\\\ P_{12}= (-3)^{12}*(-3) ^{-66} \\\\ P_{12}= (-3)^{12-66} \\\\ P_{12}= (-3)^{-54} \\\\ P_{12}= 1,72 * 10^{-26}$