Question

the product of three consecutive terms of a GP is - 64 and the first term is 4 times the third find the terms

Answer 1

HELLO DEAR,

LET THE THREE
terms of Gp be
$\frac{a}{r} \: \: \: \: \: \: \: a \: \: \: \: \: \: \: \: ar \\ = > \frac{a}{r} \times a \times ar = - 64 \\ = > {a}^{3} = - 64 \\ = > a = - 4$

now,

given that :-


first term is four times third term,

$\frac{a}{r} = 4(ar) \\ = > {r}^{2} = \frac{1}{4} \\ = > r = + - \frac{1}{2}$

when (r)= (- 1/2)

First term=
$\frac{ - 4}{ \frac{ - 1}{2} } = 8$
second term =-4

third term=-4(-1/2)

when r= 1/2

first term =
$\frac{ - 4}{ \frac{1}{2} } = - 8$
second term=

$- 4$
third term=
$( - 4 \times \frac{1}{2} ) = - 2$
i hope you dear thanks