Question

Find the sum of the first 9 terms of the geometric sequence: 0.5, 1, 2,-..

Answer 1

Answer:

S₉ = 255.5

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 = 0.5 and r = $\frac{a_{2} }{a_{1} }$ = $\frac{1}{0.5}$ = 2 , then

S₉ = $\frac{0.5(2^{9}-1) }{2-1}$

    = $\frac{0.5(512-1)}{1}$

    = 0.5(511)

    = 255.5