Question

Find the first three terms of the geometric sequence using the explicit formula: 5(2)^(n - 1)6, 18, 545, 10, 204, 8, 1610, 20, 40

Answer 1

Given:

The explicit formula is,

`5\cdot2^(\lparen n-1))`

To find:

First three terms

Step-by-step explanation:

Substituting n = 1 in the explicit formula, we get

`\begin{gathered} 5\cdot2^(1-1)=5\cdot2^0 \\ =5 \end{gathered}`

Substituting n = 2 in the explicit formula, we get

`\begin{gathered} 5\cdot2^(2-1)=5\cdot2^1 \\ =10 \end{gathered}`

Substituting n = 3 in the explicit formula, we get

`\begin{gathered} 5\cdot2^(3-1)=5\cdot2^2 \\ =20 \end{gathered}`

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.