Question

2) Determine o nº de termos da PG,
a) ( - 4, 8 ,,,,256)
b) ( 1,3,..,243)

Answer 1

Explicação passo-a-passo:

a)

• Razão

$\sf q=\dfrac{a_2}{a_1}$

$\sf q=\dfrac{8}{-4}$

$\sf q=-2$

• n° de termos

$\sf a_n=a_1\cdot q^{n-1}$

$\sf -256=(-4)\cdot(-2)^{n-1}$

$\sf (-2)^{n-1}=\dfrac{-256}{-4}$

$\sf (-2)^{n-1}=64$

$\sf (-2)^{n-1}=(-2)^6$

Igualando os expoentes:

$\sf n-1=6$

$\sf n=6+1$

$\sf n=7$

b)

• Razão

$\sf q=\dfrac{a_2}{a_1}$

$\sf q=\dfrac{3}{1}$

$\sf q=3$

• n° de termos

$\sf a_n=a_1\cdot q^{n-1}$

$\sf 243=1\cdot3^{n-1}$

$\sf 3^{n-1}=243$

$\sf 3^{n-1}=3^5$

Igualando os expoentes:

$\sf n-1=5$

$\sf n=5+1$

$\sf n=6$