Question

What is the nth term rule of the quadratic sequence below?
-5, -3,3, 13, 27, 45, 67, ...

Answer 1

`u_(n) = 2n^(2) -4n-3`

Explanation:

a +b + c = - 5 First term in sequence

3a + b = 2 Difference between first two terms

2a = 4 Difference between the difference of the first two terms and the second third terms (the difference between -5 and -3 is 2 the difference between -3 and 3 is 6; the difference between 6 and two is 4)

2a = 4 so a = 2; 3(2) + b = 2 → 6 + b = 2 so b = -4; 2 - 4 + c = -5 → -2 + c = -5 so c = -3

Answer 2

the pattern is +2, +6, +10, +14, +18 etc

so its in increment of 4

the rest is trivial

Explanation: