Question

What is the sum of the first 10 terms of the geometric sequence 4, -12, 36, -144

Answer 1

The sum of the first 10 terms of the sequence 4, -12, 36, -144 is -59058

The given geometric sequence is:

4, -12, 36, -144

The first term, a = 4

The common ratio,

$r = \frac{-12}{4}\\r = -3$

Since we are looking for the sum of the first 10 terms

The number of terms, n = 10

The sum of the first n terms of a geometric sequence is given as:

$S_n = \frac{a(1-r^n)}{1-r} \\S_n = \frac{4(1-(-3)^{10}}{1-(-3)} \\S_n = \frac{4(1-59049)}{4} \\S_n = -59048$

The sum of the first 10 terms of the sequence 4, -12, 36, -144 is -59058

Learn more here: brainly.com/question/15626828