Answer:
The first five terms are: 5,10,20,40,80
Step-by-step explanation:
The given sequence is defined explicitly as:
[tex]f(n) = 5( {2}^{n - 1} )[/tex]
We want to find the first five terms of this sequence:
For the first term, n=1,
[tex]f(1) = 5( {2}^{1- 1} ) = 5 \times {2}^{0} = 5[/tex]
When n=2,
[tex]f(2) = 5( {2}^{2 - 1} ) = 5 \times {2}^{1} = 10[/tex]
When n=3,
We have
[tex]f(3) = 5( {2}^{3- 1} ) = 5 \times {2}^{2} = 5 \times 4 = 20[/tex]
When n=4, we get:
[tex]f(n) = 5( {2}^{4- 1} ) = 5 \times {2}^{3} = 40[/tex]
When n=5,
[tex]f(5) = 5( {2}^{5- 1} ) = 5 \times {2}^{4} = 5 \times 16 = 80[/tex]
The first five terms are: 5,10,20,40,80
