Answer:
Infinite alternating sequence
Step-by-step explanation:
As we know that series is basically sum of sequence, so, the given set of numbers is not an infinite arithmetic series, finite geometric series and an infinite geometric series as it is just a sequence of numbers
Now, we need to check if [tex]-1,2,-4,8...[/tex] is an infinite alternating sequence or not .
An infinite alternating sequence is basically of form [tex](-1)^{n+1}2^n[/tex]
If we take [tex]a_n=2^n[/tex]
For n=0 , we get [tex]a_0=2^0=1[/tex]
For n=1 , we get [tex]a_1=2^1=2[/tex]
For n=2 , we get [tex]a_2=2^2=4[/tex]
For n=3 , we get [tex]a_3=2^3=8[/tex] and so on
So, we get sequence as [tex]\left ( -1 \right )^{1}2^0\,,\,\left ( -1 \right )^{2}2^{1}\,,\,\left ( -1 \right )^{3}2^{2}\,,\,\left ( -1 \right )^{4}2^{3}\,...[/tex]
i.e [tex]-1,2,-4,8...[/tex]
