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 =

 The required expression is  

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

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

Thus, the required expression is