The explicit formula for the given sequence is a(n) = 2 . (0.5)ⁿ and the first five terms are: 1, 0.5, 0.25, 0.125, 0.0625
Given the parameters:
First term, a(1) = 1, and
common ratio, r = 0.5
We are ask to find the explicit formula for the geometric sequence and generate the first five terms.
Recall that in a geometric sequence:
a(n) = a(1) . rⁿ⁻¹
Where a(n) is the nth term.
Substituting a(1) = 1 and r = 0.5:
a(n) = 1 . (0.5)ⁿ⁻¹
= (0.5)⁻¹. (0.5)ⁿ
= 2 . (0.5)ⁿ
To generate the first five terms, we can use the above explicit formula for n = 1, 2, ..., 5 or we can use a recursive procedure. Remember that in a geometric sequence:
a(n) = a(n-1) . r
Therefore,
a(1) = 1 (given)
a(2) = 1 . (0.5) = 0.5
a(3) = 0.5 . (0.5) = 0.25
a(4) = 0.25 . (0.5) = 0.125
a(5) = 0.125 . (0.5) = 0.0625
Thus, the first five terms are: 1, 0.5, 0.25, 0.125, 0.0625
Learn more about geometric sequence here:
https://brainly.com/question/24782892
#SPJ4
