Answer:
The sum is -159964.
Step-by-step explanation:
Since, the sum of a geometric sequence is,
\(S_n=\frac{a(1-r^n)}{1-r}\text{ When } |r| < 1\)
or \(S_n=\frac{a(r^n-1)}{r-1}\text{ When } |r| > 1\)
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
\(r=\frac{24}{-4}=-6\)
And, n = 7,
Since, |-6| > 1
Therefore, the sum of the given sequence is,
\(S_7=\frac{-4((-6)^7-1)}{-6-1}\)
\(=\frac{-4(-279936-1)}{-7}\)
\(=-\frac{4\times 279937}{7}\)
\(=-\frac{1119748}{7}=-159964\)
