Question

Arithmetic sequences help? I completely forgot how to do this...
Find an equation for the nth term of the arithmetic sequence.

\(a_{19}\) = -58, \(a_{21}\) = -164

Answer 1

Firstly, remember that the defining property of an arithmetic sequence is the consecutive term difference is constant. Here, you have a two term gap. So what's the common difference between successive terms?

Answer 2

subtracting 53 each term

Answer 3

That's correct. :-)

Answer 4

usually to find the difference you take the next term subtract the previous term to get the common difference

Answer 5

So, for each term you move along, you subtract another 53. This means your formula will contain -53n.

Answer 6

no!

Answer 7

that's not your common difference

Answer 8

So now we need a constant k such that:\[a_n=k-53n\]

Answer 9

The equation for a arithmetic sequence is a_n = a_1+ d(n-1)
Where n is the "nth term" and d is the difference between the the terms.

Answer 10

So what is the common difference is if not -53?

Answer 11

This is all just confusing me more... ;/

Answer 12

a_n = a_1+ d(n-1) is the standard form of arithmetic sequences.

Answer 13

-53 is d

Answer 14

All you need is the 1st term of the sequence

Answer 15

Ok, thanks for helping @swagmaster47

Answer 16

I was lagging out, do you still need help?

Answer 17

Finding a_1