Question

Evaluate each geometric series described 1-4+16-64...., n=6

Answer 1

Answer:

-819

Step-by-step explanation:

This is Geometric series with first term as '1' and a common ratio of '-4' (-4÷1 = -4)

At n=5, the term is (-64×-4) = 256

At n=6, the term is (256×-4) = -1024

1-4+16-64+257-1024 = -819

Answer 2

Answer:

- 819

Step-by-step explanation:

The sum to n terms of a geometric series is

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

where a is the first term and r the common ratio

Here a = 1 and r = - 4 ÷ 1 = - 4, thus

$S_{6}$ = $\frac{1((-4)^6-1)}{-4-1}$ = $\frac{4096-1}{-5}$ = $\frac{4095}{-5}$ = - 819