Question

Which of the following is the missing term of the geometric sequence in which a1= 2 and a3 = 200?

Answer 1

a2 = 20.
The formula is a(n+1) = 10a(n)

Answer 2

20

Explanation:

Given that the first term of a geometric sequence is 2 and third term is 200.

We have to find the middle term

A geometric sequence will have terms of the form

`a,ar,ar^2,....`

Since first term is 2,
`a=2`...i

Since third term is 200,
`ar^2 =200`...ii

Divide equation ii by i to get

`r^2 =100\\r=10`

Because increasing sequence, r cannot be negative so only positive value is take.

II term =
`ar=2(10)=20`

Hence missing term is 20