A geometric sequence is characterized by a common ratio.
The next term of the sequence is 20.25
First, we calculate the common ratio (r)
[tex]\mathbf{r = \frac{T_2}{T_1}}[/tex]
So, we have:
[tex]\mathbf{r = \frac{0.75}{0.25}}[/tex]
[tex]\mathbf{r = 3}[/tex]
The nth term of the GP is calculated using:
[tex]\mathbf{T_n = T_1 \times r^{n-1}}[/tex]
Where:
[tex]\mathbf{T_1= 0.25}[/tex]
[tex]\mathbf{n = 5}[/tex]
So, we have:
[tex]\mathbf{T_5 = 0.25 \times 3^{5-1}}[/tex]
[tex]\mathbf{T_5 = 0.25 \times 3^4}[/tex]
[tex]\mathbf{T_5 = 20.25}[/tex]
Hence, the next term of the sequence is 20.25
Read more about geometric sequence at:
https://brainly.com/question/18109692
