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

Answer:

20

Step-by-step 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