What is the 32nd term of the arithmetic sequence where a1 = 12 and a13 = −60?

I can't seem to find the value of d no matter how hard I try and I keep getting weird answers.

Question

What is the 32nd term of the arithmetic sequence where a1 = 12 and a13 = −60?

I can't seem to find the value of d no matter how hard I try and I keep getting weird answers.

fortytherapper · Answer

So when a changed by 13 minus one (13-1), the number changed by negative 60 minus 12 (-60-12)

lerenstudy · Answer

Wouldn't it change by positive 12 since a1 is positive and a13 is negative?

lerenstudy · Answer

Would the difference happen to be -6 in this?

texaschic101 · Answer

yes...d = -6

lerenstudy · Answer

Okay, so then if I just subtract 12 by (32-1)(-6) would I get what I need? I'm not quite sure of the formula I need

lerenstudy · Answer

Because I'm getting -174. Is that right?

fortytherapper · Answer

I got -174 also. I never got to study this, so I just made up a formula

lerenstudy · Answer

Alright, I think that's right, so I'll go with it. Thanks a bunch

fortytherapper · Answer

We're looking for X, which is a32

So I did

X - (-60)
----------- = -6
32-13

X - a13
------------ = D
32-13

Then solved for D. And no problem, anytime

fortytherapper · Answer

I mean solves for X

lerenstudy · Answer

Alright, that gets -174 too. Thank you!