Question

Given the geometric sequence where a_1 = 3 and r = √2 find a_9

A.] 48
B.] 48√2
C.] 64
D.] 64√2

Answer 1

To find n-therm of a geometric sequence, we are going to use the formula
`a_(n) =a _(1) r^(n-1)`
where:

`a_(n)` is the term we are looking for

`a _(1)` is the first term

`r` is the ratio

`n` is the position of the number in the sequence

From the question we now that
`a _(1) =3`,
`r= √(2)`, and
`n=9`. Lets replace those values into our formula to get:

`a _(9) =3( √(2) )^(9-1)`

`a_(9) =3 √(2) ^(8)`

`a_(9) =48`

We can conclude that in our geometric sequence
`a_(9) =48`; therefore, the answer is A.