Given:
The given geometric series is [tex]2 + 3 + 4.5+ 6.75 + ...[/tex]
We need to determine the value of r and a₁
Value of a₁:
The term a₁ denotes the first term of the geometric series.
Hence, from the given series, the first term of the series is 2.
Thus, a₁ = 2.
Therefore, the value of a₁ is 2.
Value of r:
The term r denotes the common ratio between the terms in the geometric series.
The value of r is given by
[tex]r=\frac{3}{2}=1.5[/tex]
[tex]r=\frac{4.5}{3}=1.5[/tex]
[tex]r=\frac{6.75}{4.5}=1.5[/tex]
Thus, the value of r is 1.5
