Question

Find r for the geometric series s5=244 a1=4 and a5=324

Answer 1

-3

Explanation:

an = a1·r^(n-1) . . . . . . general term of a geometric sequence

a5 = 324 = 4·r(5-1) . . . specifically, the 5th term

81 = r^4 . . . . . . . . . . . divide by 4

Since the sum of 5 terms is less than the 5th term, the value of r must be negative:

`r=-\sqrt[4]{81}=-3`