Question

Please see attached.

Answer 1

What kind of the sequence is it?

Answer 2

arithmetic

Answer 3

The general term of the arithmetic sequence looks like
\[a_n=a_1+(n-1)d\]All you need is to find a_1 and d.
\[a_7=79=a_1+(7-1)d\]\[a_{12}=64=a_1+(12-1)d\]Two linear equations and 2 variables, solve it and put values of a1 and d into the first formula.

Answer 4

like system of equation?

Answer 5

Sure, but instead of x and y you have a_1 and d.

Answer 6

legend.

Answer 7

Can you solve it? I want to be sure that you've solve it correctly.

Answer 8

do I solve it just like a systems?

Answer 9

Yes!

Answer 10

substitution or elimination

Answer 11

Anything you like or what is more simple for you.

Answer 12

Hm..Lets try once again. The general term of the sequence is \[u_n=u_1+(n-1)d\]u1 is the first term of the sequence and d is the difference
You know just u7 and u12 and want to know the general term for any n. So you need to find u1 and d and then put them in the first formula. How to get u1 and d? Just let n=7 and n=12 and get a system of 2 linear equations
\[u_7=79=u_1+6d\]\[u_{12}=64=u_1+11d\]All you need is to solve it!

Answer 13

right I got d=-3 and u1=96

Answer 14

Check your result by putting it into one of your equations. I think you've made a mistake.

Answer 15

my bad u1=97 and the nth term will be -3n+100

Answer 16

Now you're right!

Answer 17

thanks for your help man.

Answer 18

If you have any other questions - ask me.