Question

Find the sum of the following geometric sequences a) 6 terms (-4, 12, -36,...)​

Answer 1

Answer:

S₆ = 728

Step-by-step explanation:

the sum to n terms of a geometric sequence is

$S_{n}$ = $\frac{a_{1}(r^{n}-1) }{r-1}$

where a₁ is the first term and r the common ratio

here a₁ = - 4 and r = $\frac{a_{2} }{a_{1} }$ = $\frac{12}{-4}$ = - 3 , then

S₆ = $\frac{-4((-3)^{6}-1) }{-3-1}$

    = $\frac{-4(729-1)}{-4}$

    = 729 - 1

    = 728