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

Question

anonymous · Answer

$$a_{1}=28,d=10$$

jhannybean · Answer

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

anonymous · Answer

This?
$$a_{n} = a + (n - 1)d.$$

jhannybean · Answer

Good :) Yes that is it.

jhannybean · Answer

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

anonymous · Answer

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

jhannybean · Answer

Yes.

jhannybean · Answer

$a=a_1=28$

anonymous · Answer

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

jhannybean · Answer

Good :)

jhannybean · Answer

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

anonymous · Answer

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

jhannybean · Answer

Haha yeah, for me as well!!