Question

find the sum of the geometric series 8 -4 2 -1 ....where there are 5 terms

Answer 1

Answer:

11/2

Step-by-step explanation:

Given, G.P

8, -4, 2, -1, . . . , then

a = 8, and r = -4/8 = -1/2

A/Q,

$sum \: of \: n \: terms \: = \frac{a(1 - {r}^{n} )}{1 - r} \\ n = 5 \\ sum \: of \: 5 \: terms \: = \frac{8(1 - { (\frac{ - 1}{2} )}^{5}) }{1 - ( \frac{ - 1}{2}) } \\ = \frac{8(1 + \frac{1}{32} )}{1 + \frac{1}{2} } \\ = \frac{8( \frac{33}{32} )}{ \frac{3}{2} } = \frac{ \frac{33}{4} }{ \frac{3}{2} } = \frac{33}{4} \times \frac{2}{3} = \frac{11}{2}$