Question

Work out the formula for the nth term of the
quadratic sequence:
19, 15, 9, 1...

Answer 1

Tn = -n^2 - n + 21

Answer 2

Tn = -n^2 - n + 21 is the formula for the nth term.

Explanation:

The second differences are all equal in this quadratic sequence.

Now, the quadratic sequence has a formula of Tn = an^2 + bn + c

Find the value of a in an^2 by dividing the difference by 2:

-2/2 = -1

a = -1

Since T1 is 19 and T2 is 15 we can put that into the equation and simplify:

b + c = 20

2b + c = 19

Thus, b = -1 , c = 19 and the general formula for the nth term is Tn = -n^2 - n + 21