Question

If r = 4 and ^a8 = 100, what is the first term of the geometric
sequence?

Answer 1

The first term of the geometric sequence is 0.0061

Answer 2

The first term of the geometric sequence is 0.0061

Explanation:

The general form of geometric sequence is a, ar, ar²,ar³,.......

where,

• a is the first term of the sequence.
• r is the common ratio. Here, the common ratio r = 4.
• The 8th term of the sequence is 100. Hence n = 8.

The formula to find the nth term of the geometric sequence is given by :

⇒
`n_(th) term = ar^(n-1)`

⇒
`8_(th)term = a*4^(8-1)`

⇒
`100 = a * 4^(7)`

⇒
`100 = a * 16384`

⇒
`a = (100)/(16384)`

⇒ a = 0.0061

Therefore, the first term of the geometric sequence is 0.0061