Answer
$a_{1} = -7, r= 2$
Work Step by Step
Given,
$a_{3} = -28$
$a_{4} = -56$
In geometric sequence, common ratio,
$r = \frac{a_{n}}{a_{n-1}}$
$r = \frac{a_{4}}{a_{3}} = \frac{-56}{-28} =2$
To find $a_{1},$
$a_{3} = a_{1} . r^{3-1} $ using $a_{n} = a_{1} . r^{n-1} $
$a_{3} = a_{1} . r^{2} $
Using $r$ and $a_{3}$ values,
$-28= a_{1} .(2)^{2} $
$-28 = a_{1} .(4) $
$a_{1} = \frac{-28}{4}$
$a_{1} = -7$
