Respuesta :
The first five terms of the sequence is 1, –2, 4, –8, 16.
Solution:
Given explicit formula is [tex]a_n=(-2)^{n-1}[/tex].
To find the first five terms of the sequence, substitute n = 1, 2, 3, 4 and 5 in the given explicit formula.
For n = 1, we get
[tex]a_1=(-2)^{1-1}[/tex]
[tex]=(-2)^{0}[/tex]
= 1 (Using exponent rule [tex]a^0=1[/tex])
For n = 2, we get
[tex]a_2=(-2)^{2-1}[/tex]
[tex]=(-2)^{1}[/tex]
[tex]=-2[/tex]
For n = 3, we get
[tex]a_3=(-2)^{3-1}[/tex]
[tex]=(-2)^{2}[/tex]
= 4
For n = 4, we get
[tex]a_4=(-2)^{4-1}[/tex]
[tex]=(-2)^{3}[/tex]
= –8
For n = 5, we get
[tex]a_5=(-2)^{5-1}[/tex]
[tex]=(-2)^{4}[/tex]
= 16
Hence, the first five terms of the sequence is 1, –2, 4, –8, 16.
