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

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gmany gmany · Answer 1 · 2018-08-11T00:54:22+02:00

The formula of a sum of the geometric sequence:

[tex]S_n=\dfrac{a_1(1-r^n)}{1-r}[/tex]

We have:

[tex]a_1=-3(4)^{1-1}=-3(4)^0=-3\\\\r=4\\\\n=5[/tex]

Substitute:

[tex]S_5=\dfrac{-3(1-4^5)}{1-4}=\dfrac{-3(1-1024)}{-3}=\dfrac{-3(-1023)}{-3}=-1,023[/tex]

Answer: A) -1,023

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eudora eudora · Answer 2 · 2019-03-04T18:30:13+01:00

Answer:

Option A. -1023

Step-by-step explanation:

If we form the finite geometric sequence by using expression [tex]-3.4^{(n-1)}[/tex] 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 = [tex]a.\frac{(1-r^{n})}{1-r}[/tex]

Here a = -3

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

n = 5

Therefore sum of the sequence = [tex](-3).\frac{(1-4^{5}) }{1-4}= \frac{(-3).(-1023)}{(-3)}=-1023[/tex]

Option A is the answer.