Question

The first three terms of a sequence are

given. Round to the nearest thousandth
(if necessary).
4, 8, 12,..
Find the 40th term

Answer 1

Explanation:

Recall the formula for an arithmetic sequence:
`a_(n) =a_(1) +d(n-1)`

Where d is the common difference and a_1 is the first term of the sequence.

You are given :

a_1=4

a_2=8

a_3=12

Next is to find the common difference d.

To find the common difference, take the next term and subtract it from the current term.

a_2-a_1=8-4=4

Let try the next term start at a_2

a_3-a_2=12-8 =4

Do you see the pattern?

The patter is going up by 4 each time. So the common difference is 4 i.e d=4

Now we just need to plug into the generalize formula above and get

`a_(n)=4+4(n-1)`

The question asked for the 40th term. Plug 40 into the formula and you will get:

`a_(40)=4+4(40-1)=160`

I hope this helps!