Question

Find the first four terms of the sequence given by the following.1a₁=5 (4)"-¹, n=1, 2, 3...

Answer 1

Given the sequence:

`a_n=5(4)^(n-1)`

Therefore, the first four terms are:

n = 1

`a_1=5(4)^(1-1)=5(4)^0=5(1)=5`

n = 2

`a_2=5(4)^(2-1)=5(4)^1=5(4)=20`

n = 3

`a_3=5(4)^(3-1)=5(4)^2=5(16)=80`

n = 4

`a_4=5(4)^(4-1)=5(4)^3=5(64)=320`

Answer: 5, 20, 80, 320