Answer:
The sum is -159964.
Step-by-step explanation:
Since, the sum of a geometric sequence is,
[tex]S_n=\frac{a(1-r^n)}{1-r}\text{ When } |r| < 1[/tex]
or [tex]S_n=\frac{a(r^n-1)}{r-1}\text{ When } |r| > 1[/tex]
Where, a is the first term of the sequence,
r is the common ratio,
n is the number of terms,
Given, sequence,
–4, 24, –144, …....., up to 7 terms,
Thus, a = - 4
[tex]r=\frac{24}{-4}=-6[/tex]
And, n = 7,
Since, |-6| > 1
Therefore, the sum of the given sequence is,
[tex]S_7=\frac{-4((-6)^7-1)}{-6-1}[/tex]
[tex]=\frac{-4(-279936-1)}{-7}[/tex]
[tex]=-\frac{4\times 279937}{7}[/tex]
[tex]=-\frac{1119748}{7}=-159964[/tex]
