Answer: For the given geometric series, the first term is [tex]a_1=2[/tex] and the common ratio is [tex]r=-1.[/tex]
Step-by-step explanation: We are given to find the values of [tex]a_1[/tex] and [tex]r[/tex] of the following geometric series:
[tex]2-2+2-2+2-~.~.~..[/tex]
We know that
[tex]a_1[/tex] is the first term and [tex]r[/tex] is the common ratio of the given geometric series.
We can see that the first term of the given geometric series is 2.
So. we must have
[tex]a_1=2.[/tex]
Also, common ratio is found by dividing a term by its preceding term.
Therefore, the common ratio [tex]r[/tex] of the given geometric series is
[tex]r=\dfrac{-2}{2}=\dfrac{2}{-2}=~.~.~.~=-1.[/tex]
Thus, for the given geometric series, the first term is [tex]a_1=2[/tex] and the common ratio is [tex]r=-1.[/tex]
