Answer: 258
Step-by-step explanation:
Since, the sum of GP is,
[tex]S_{n}=\frac{a(r^n-1)}{r-1}[/tex]
where r is the common ratio,
a is the first term,
n is the number of term,
Here, series is, 6, -12, 24, -48, _ _ _ _
Which is a GP ( Because there is common ratio in the given consecutive terms )
So, for the above series, a = 6, r = [tex]\frac{6}{-12}=-2[/tex] and n = 7,
⇒ [tex]S_{7}=\frac{6(-2^7-1)}{-2-1}[/tex]
⇒ [tex]S_{7}=\frac{6(-128-1)}{-3}[/tex]
⇒ [tex]S_{7}=\frac{6(-129)}{-3}[/tex]
⇒ [tex]S_{7}=\frac{774}{3}=258[/tex]
Thus, the sum of the 7 terms of the given series is 258.
