Question

What are the first four terms of the geometric sequence an=2 an-1 and a1=3​

Answer 1

B.
`3,6,12,24`

Explanation:

We are given that

`a_n=2a_(n-1)`

`a_1=3`

We have to find the first four terms of G.P

Substitute n=2

`a_2=2a_1=2(3)=6`

Substitute n=3

`a_3=2a_2=2(6)=12`

Substitute n=4

`a_4=2a_3=2(12)=24`

Hence, the first four terms of G.P are given by

`3,6,12,24`

Option B is true.

Answer 2

3, 6, 12, 24

Explanation:

This is a recursive formula which allows the next term in a sequence to be found from the previous term in the sequence

Given

`a_(n)` = 2
`a_(n-1)` with a₁ = 3, then

a₂ = 2 × a₁ = 2 × 3 = 6

a₃ = 2 × a₂ = 2 × 6 = 12

a₄ = 2 × a₃ = 2 × 12 = 24

Thus the first 4 terms are 3, 6, 12, 24