For each of the finite geometric series given below, indicate the number of terms in the sum and find the sum. For the value of the sum, enter an expression that gives the exact value, rather than entering an approximation.

A. 5+5 (0.15) + 5 (0.15) 2+⋯+5 (0.15) 14

number of terms =

value of sum =

B. 5 (0.15) 4+5 (0.15) 5+5 (0.15) 6+⋯+5 (0.15) 9

number of terms =

value of sum =

a) Number of terms = 15

Value of sum =

(b) Number of terms = 6

Value of sum

Step-by-step explanation:

A.

nth term,

a=5, r=

Simce the bases are the same, the powers are equal.

n-1=14

n=14+1=15

Number of terms =

15

Value of sum =

B.

nth term,

a=,

Simce the bases are the same, the powers are equal.

4+n-1=9

n=9+1-4=6

Number of terms =

6

Value of sum

NOTE: For the sum, we desire an expression that gives the exact value, rather than entering an approximation