Question

Consider the following geometric series. Rewrite the series using sigma notation. 4-10+25-62.5+156.25-390.625

Answer 1

Answer:

$\sum_{n=1}^{n=6} 4(\frac{-5}{2} )^{n-1}$  

Step-by-step explanation:

We are given the geometric series $4 + -10+ 25+ -62.5+ 156.25+ -390.625$

General geometric series is of the form

$a, ar, ar^2, ar^3, ar^4,\text{ and so on}$, where a is the first term and r is the common ration.

The common ratio for given geometric series is $\frac{\text{Second Term}}{\text{First Term}}$ = $\frac{-10}{4} = \frac{-5}{2}$

$a = 4\\r = \frac{-5}{2}$

To write the series in summation form we use:

$\sum_{k=0}^{k=n} a(r)^{k}$

Thus, the given geometric series is

$\sum_{n=1}^{n=6} 4(\frac{-5}{2} )^{n-1}$

Answer 2

Answer:

See below.

Step-by-step explanation:

The common ratio = -10/4 = -5/2 and the first term is 4.

The sigma notation is:

n=6

∑       4(-5/2)^n-1.   (answer).

n=1