To find the first three terms of the sequence defined by the formula [tex]\( A_n = \left(\frac{y}{4}\right)^n \)[/tex], follow these steps:
1. Determine the 1st Term:
For [tex]\( n = 1 \)[/tex]:
[tex]\[
A_1 = \left( \frac{y}{4} \right)^1 = \frac{y}{4}
\][/tex]
For simplicity, let's assume [tex]\( y = 1 \)[/tex]:
[tex]\[
A_1 = \frac{1}{4} = 0.25
\][/tex]
2. Determine the 2nd Term:
For [tex]\( n = 2 \)[/tex]:
[tex]\[
A_2 = \left( \frac{y}{4} \right)^2 = \left( \frac{y}{4} \right) \times \left( \frac{y}{4} \right) = \left( \frac{1}{4} \right)^2 = \frac{1}{16}
\][/tex]
Again, using [tex]\( y = 1 \)[/tex]:
[tex]\[
A_2 = \frac{1}{16} = 0.0625
\][/tex]
3. Determine the 3rd Term:
For [tex]\( n = 3 \)[/tex]:
[tex]\[
A_3 = \left( \frac{y}{4} \right)^3 = \left( \frac{y}{4} \right) \times \left( \frac{y}{4} \right) \times \left( \frac{y}{4} \right) = \left( \frac{1}{4} \right)^3 = \frac{1}{64}
\][/tex]
Using [tex]\( y = 1 \)[/tex]:
[tex]\[
A_3 = \frac{1}{64} = 0.015625
\][/tex]
Thus, the first three terms of the sequence are:
[tex]\[
A_1 = 0.25, \quad A_2 = 0.0625, \quad A_3 = 0.015625
\][/tex]
