Answer:
Explicit formula for the sequence is [tex]a_n=(-1)^{n+1}2^{n-1}[/tex]
[tex]a_{10}=-512[/tex]
Step-by-step explanation:
Given: Sequence is [tex]1,-2,4,-8,16,...[/tex]
To find: explicit formula for the sequence and the [tex]10^{th}[/tex] term of the sequence
Solution:
A sequence is an ordered list of numbers which repetitions are allowed and order does matter.
[tex]a_1=(-1)^{1+1}\left [ 2^{(1-1)} \right ]=1\\a_2=(-1)^{2+1}\left [ 2^{(2-1)} \right ]=-2\\a_3=(-1)^{3+1}\left [ 2^{(3-1)} \right ]=4\\a_4=(-1)^{4+1}\left [ 2^{(4-1)} \right ]=-8\\a_5=(-1)^{5+1}\left [ 2^{(5-1)} \right ]=16[/tex]
So, explicit formula for the sequence is [tex]a_n=(-1)^{n+1}2^{n-1}[/tex]
To find the [tex]10^{th}[/tex] term of the sequence, put n = 10
[tex]a_{10}=(-1)^{10+1}\left [ 2^{(10-1)} \right ]\\=(-1)^{11}2^9\\=-1(2^9)\\=-512[/tex]
