Write a formula that will yield the nth term of the sequence: 3,-2,-7,-12

-5n + 8

Step-by-step explanation:

1. What is the difference?

The sequence goes down by 5. This means that the formula will have - 5n in it.

2. Work out the term before the first term.

The first term is 3, and we know that the sequence goes up by 5. So, to get the term before 3 we would add 5.

3 + 5 = 8 Remember, this is positive 8. (+8)

3. Put that term at the end of the equation.

We have - 5n already and we just worked out the term before the first one which is positive 8 - so put that at the end of the equation.

-5n + 8 This is our answer!

Just to prove it works:

Substitute: n = term

Lets see if we can get the 3rd term which is - 7. (n = 3)

-5 (3) + 8

-15 + 8 = - 7

See, it works!