Question

This explicit formula defines a sequence for integer values of n greater than or equal to 1:

an=
1
2
n–1
Find the first three terms in the sequence.
Write your answers as integers or fractions in simplest form.
a1
=
a2
=
a3
=

Answer 1

The first three terms of the sequence defined by the formula
`a_n=-4+7^{(n-1)` are a_1=-3, a_2=3, and a_3=45.

The student is asked to find the first three terms in the sequence defined by the explicit formula
`a_n=-4+7^{(n-1)` for integer values of n ≥ 1.

To find a_1, we substitute n=1 into the formula:

`a_1=-4+7^((1-1))=-4+7^0\\a_1=-4+1\\a_1=-3.`

For a_2, substitute n=2:

`a_2=-4+7^((2-1))\\a_2=-4+7^1\\a_2=-4+7\\a_2=3.`

Lastly, for a_3, we use n=3:

`a_3=-4+7^((3-1))\\a_3=-4+7^2\\a_3=-4+49\\a_3=45.`

Therefore, the first three terms in the sequence are a_1=-3, a_2=3, and a_3=45.

The probable question may be:

This explicit formula defines a sequence for integer values of n greater than or equal to 1.

a_n=-4+7^(n-1)

Find the first three terms in the sequence. Write your answers as integers or fractions in simplest form.

a_1=_____

a_2=_____