Question

Find the sum of a finite geometric sequence from n = 1 to n = 5, using the expression -3(4)^n - 1.

A) -1,023
B) 1,223
C) 1,023
D) -4,374

Answer 1

The formula of a sum of the geometric sequence:

`S_n=(a_1(1-r^n))/(1-r)`

We have:

`a_1=-3(4)^(1-1)=-3(4)^0=-3\\\\r=4\\\\n=5`

Substitute:

`S_5=(-3(1-4^5))/(1-4)=(-3(1-1024))/(-3)=(-3(-1023))/(-3)=-1,023`

Answer: A) -1,023

Answer 2

Option A. -1023

Explanation:

If we form the finite geometric sequence by using expression
`-3.4^((n-1))` by putting n = 1, 2, 3, 4, 5.

Sequence will be = -3, -12, -48, -192, -768

Now we can either do the total of all numbers of the sequence or use the formula to calculate the sum.

Total of terms = (-3) + (-12) + (-48) + (-192) + (-768) = -1023

Or by using formula

Sum =
`a.((1-r^(n)))/(1-r)`

Here a = -3

r = (-12)/(-3) = 4

n = 5

Therefore sum of the sequence =
`(-3).((1-4^(5)) )/(1-4)= ((-3).(-1023))/((-3))=-1023`

Option A is the answer.