Question

Given the first term and the common difference of an arithmetic sequence find the first three terms and the explicit formula.

Answer 1

\[a_{1}=28,d=10\]

Answer 2

First off, do you know the equation for an arithmetic sequence?/

Answer 3

This?
\[a_{n} = a + (n - 1)d.\]

Answer 4

Good :) Yes that is it.

Answer 5

Now we are looking for the first 3 terms, that can be written as \(n=3\)

Answer 6

So I know that n=3 and d=10
Does a=28 in the equation?

Answer 7

Yes.

Answer 8

\(a=a_1=28\)

Answer 9

So I have
\[a_{3}=28+(3-1)10\]
\[a_{3}=28+(2)10\]
\[a_{3}=28+20\]
\[a_{3}=48\]

Answer 10

Good :)

Answer 11

Now to find the explicit formula, we're basically writing the formula for \(a_3\) with all our terms without really solving for anything.

Answer 12

Alright thanks! I get it now! It's been a while!

Answer 13

Haha yeah, for me as well!!