For the geometric sequence whose second term is 64 and whose fifth term is -8, find the value of the 9th term

geometric-sequence

#1

For the geometric sequence whose second term is 64 and whose fifth term is -8, find the value of the 9th term.

Answer:

A2 = ar = 64
A5 = a
r^4 = -8
Where a is the first term and r is the coming reason of the geometric series
Now A4/A2 = ar^4/ar
=> r^3 = -8/64
=> r^3 = -1/8
=> r = -1/2

Now, a*r = 64
=> a = 64/r
=> a = -128

A9 = a*r^8 = -128/256 = -1/2