Question

Geometric series mastery test

Plato/edumentum

Answer 1

183

Explanation:

it is clearly a geometric sequence.

the common ratio of multiplication factor is -3.

3 × -3 = -9

-9 × -3 = 27

27 × -3 = -81

-81 × -3 = 243

the sum of these first 5 terms is

3 - 9 + 27 - 81 + 243 = 183

FYI - there is a formula to add the first n terms of a geometric sequence :

Sn = a1(1 - r^n)/(1 - r)

if r < 1 (like in our case -3).

in our case

S5 = 3(1 - (-3)⁵)/(1 - -3) = 3(1 - -243)/4 / 3×244/4 = 3×61 = 183

Answer 2

The sum of the first five terms of the Sum of Geometric Series 3, -9, 27, -81, ... is obtained by simply adding the terms, resulting in 183.

The sum of the first five terms in the geometric series 3, -9, 27, -81, ... can be found by simply adding the terms together.

The series is a geometric progression with a common ratio of -3, since each term is -3 times the previous one.

To find the sum, we add:

3 + (-9) + 27 + (-81) + 243 = 3 - 9 + 27 - 81 + 243

Now, combining the terms we get:

-6 + 27 - 81 + 243 = 183

So, the sum of the first five terms of the series is 183.

The probable question may be:

What is the sum of first five terms in the series

3+(-9)+27+(-81)+..........

A. 61

B. -9

C. 183

D. 243