Question

Write an expression that gives the requested sum. The sum of the first 16 terms of the geometric sequence with first term 5 and common ratio 4

s_36 =

Answer 1

Answer: The required expression is

`S_(16)=(5(4^(16)-1))/(3).`

Step-by-step explanation: We are given to write an expression that gives the following sum :

the sum of first 16 terms of a geometric sequence with first term 5 and common ratio 4.

We know that

the sum of first n terms of a geometric sequence with first term a and common ratio r with |r| > 1 is given by

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

For the given geometric sequence, we have

first term, a = 5 and common ratio, r = 4.

So, |r| = |4| = 4 > 1.

Therefore, the required expression for the sum of first 16 terms is given by

`S_(16)=(5(4^16)-1)/(4-1)=(5(4^(16)-1))/(3)`

Thus, the required expression is
`S_(16)=(5(4^(16)-1))/(3).`