Question

If a[1]=4 and r=2, what are the first four terms of the geometric sequence?

Answer 1

`4, 8, 16, 32`

Explanation:

Recall that the geometric sequence formula is written as:

`color(blue)(|bar(ul(color(white)(a/a)t_n=ar^(n-1)color(white)(a/a)|)))`

where:
`t_n=`term number
`a=`first term
`r=`common ratio
`n=`number of terms

Determining the First Four Terms
`1`. Since the value of `a` has already been given, the first term is `4`.

`color(green)(|bar(ul(color(white)(a/a)t_1=4color(white)(a/a)|)))`

`color(red)(rArr)`Sequence thus far: `4,...`

`2`. Using the geometric sequence formula, substitute your known values to determine the second term.

`t_n=ar^(n-1)`

`t_2=4(2)^(2-1)`

`t_2=4(2)^1`

`color(green)(|bar(ul(color(white)(a/a)t_2=8color(white)(a/a)|)))`

`color(red)(rArr)`Sequence thus far: `4,8,...`

`3`. Repeat for the third term.

`t_n=ar^(n-1)`

`t_3=4(2)^(3-1)`

`t_3=4(2)^2`

`t_3=4(4)`

`color(green)(|bar(ul(color(white)(a/a)t_3=16color(white)(a/a)|)))`

`color(red)(rArr)`Sequence thus far: `4,8,16,...`

`4`. Repeat for the fourth term.

`t_n=ar^(n-1)`

`t_4=4(2)^(4-1)`

`t_4=4(2)^3`

`t_4=4(8)`

`color(green)(|bar(ul(color(white)(a/a)t_4=32color(white)(a/a)|)))`

`color(red)(rArr)`Sequence thus far: `4, 8, 16, 32`

`:.`, the first four terms of the sequence are `4, 8, 16, "and"` `32`.