Answer :
Given:
The explicit formula is,
[tex]5\cdot2^{\lparen n-1)}[/tex]To find:
First three terms
Explanation:
Substituting n = 1 in the explicit formula, we get
[tex]\begin{gathered} 5\cdot2^{1-1}=5\cdot2^0 \\ =5 \end{gathered}[/tex]Substituting n = 2 in the explicit formula, we get
[tex]\begin{gathered} 5\cdot2^{2-1}=5\cdot2^1 \\ =10 \end{gathered}[/tex]Substituting n = 3 in the explicit formula, we get
[tex]\begin{gathered} 5\cdot2^{3-1}=5\cdot2^2 \\ =20 \end{gathered}[/tex]Hence the first three terms of the geometric sequence are 5, 10, and 20.
Final answer:
The first three terms of the geometric sequence are 5, 10, and 20.