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

**Solution:**

In a Geometric Sequence, each term is found by multiplying the previous term by a constant. a, ar, ar^{2}, ar^{3}, ...

Given geometric expression -3(4)^{n} - 1 from n = 1 to 5.

To find the sum of geometric expression from n = 1 to n = 5 is

S\(_n\) = \(\sum_{n=1}^{5} -3(4)^n - 1\)

S\(_n\) = - 3(4)^{1} - 1 - 3(4)^{2} - 1 - 3(4)^{3} - 1 - 3(4)^{4} - 1 - 3(4)^{5} - 1.

S\(_n\) = - 5 - 3(4 + 4^{2}+ 4^{3}+ 4^{3}+ 4^{5} )

Consider the the geometric progression inside the brackets. Here a = 4 and n =5, r = 4

sum of gp if r >1 =\(\dfrac{a(r)^{n}-1}{r-1}\),

S\(_n\)= - 5 - 3(4(4)^{5 }-1]/ 3)

S\(_n\)= - 5 - 3(1364)

S\(_n\)=-4097

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

**Summary: **

The sum of a finite geometric sequence from n = 1 to n = 5, using the expression - 3(4)^{n} - 1 is -4097.