Answer:
Tn = -n^2 - n + 21 is the formula for the nth term.
Step-by-step 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
