What is the 35th term of the arithmetic sequence where a1 = 13 and a17 = -35 ?

-89
-86
-83
-80

Question

What is the 35th term of the arithmetic sequence where a1 = 13 and a17 = -35 ?
 	
	-89
	-86
	-83
	-80

anonymous · Answer

$a_1 = a_1$

$a_2 = a_1 + d$

$a_3 = a_2 + d = a _1 + d + d = a_1 + 2d$

$a_n = a_1 + (n - 1)d$               (Eq. 1)

Use $a_1 = 17$ and $a_{17} = 35$ in Eq. 1 to find d.

Then use your d and $a_1$ to find $a_{35} $ using Eq. 1.

anonymous · Answer

I'm still kind of confused.  Would you be able to walk me through it? I don't really get how to plug the numbers in. @MaxwellSmart

anonymous · Answer

Use the formula I called Eq. 1.

Here it is:

$a_n = a_1 + (n - 1)d$

You are given a1 = 13 and a17 = -35. 

Let's write the formula for a17:

$a_{17} = a_1 + (17 - 1)d$

$a_{17} = a_1 + 16d$

Now we plug in the values of a1 and a17:

$-35 = 13 + 16d$

Can you solve for d?

anonymous · Answer

does d= -3?

anonymous · Answer

Correct.
Now that you have the correct d, use Eq. 1 again.
This time write it for $\large a_{35} $.
Then use the a1 you were given and the d you found.

anonymous · Answer

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