Question

What is the value of the 24th term in the following arithmetic sequence?

-9, -2, 5, 12, ...



152

-170

170

-200
Please Explain how to get the answer! :)

Answer 1

If you look at each of the four given numbers in the sequence as the following pairs, a pattern emerges:

-9, -2
-2, 5
5, 12

Can you see something similar among these three pairs?

Answer 2

Yes, I do.

Answer 3

Well, if you've identified the pattern, then continue it, assuming that -9 is the first term in the sequence, and write out the sequence to the 24th term. That's your answer.

Answer 4

So, whatever you do to -9 to get -2, -2 to get 5, and 5 to get 12, repeat on 12 to get the next term, then on that term to get the term after that, and so on.

Answer 5

But im given a formula to find out the answer.

Answer 6

an = a1 + d(n - 1)

Answer 7

Okay, that's more complicated than it needs to be, but it works.

an = The value of the nth term
a1 = The first term in the sequence
d = The difference between each successive term in the sequence
n = The term number

Answer 8

okay I understand that.

Answer 9

So now you can plug in the values for a1, d, and n to get the answer. Since you want the value of the 24th term, n=24.

Answer 10

a1= 9 + 7(n-1) but n is 24 so its A1=9+161 Is that right?

Answer 11

a1 is actually -9

Answer 12

Whoops, my mistake.

Answer 13

You're very close. The variable on the left side of the formula is actually an.

Answer 14

Whoops, Haha I'm new to this. If you can't tell.

Answer 15

You're actually doing better than most, but everyone learns at a different rate.

Answer 16

The answer is 152?

Answer 17

Yep, nicely done.

Answer 18

Thank you! :)

Answer 19

You're very welcome! It was a pleasure helping you. Let me know if you have any other questions.