Question

Evaluate the geometric series. Please help me out!!!

Answer 1

Answer:

- 1364

Step-by-step explanation:

The n th term of a geometric series is

$a_{n}$ = a$(r)^{n-1}$

where a is the first term and r the common ratio

4$(-2)^{n-1}$ ← is an n th term

with a = 4 and r = - 2

The sum to n terms of a geometric series is

$S_{n}$ = $\frac{a(r^{n}-1) }{r-1}$, thus

$S_{10}$ = $\frac{4((-2)^{10}-1) }{-2-1}$

      = $\frac{4(1024-1)}{-2-1}$

      = $\frac{4(1023)}{-3}$

      = $\frac{4092}{-3}$

      = - 1364