Everything Maths Grade 11

5.2 CHAPTER 5. QUADRATIC SEQUENCES

Step 2 : Find the second differences between the terms

7 11 15

+4 +4

So the second differenceis 4.

Continuing the sequence, the differences between each term will be:

...15 19 2 3...

+4 +4

Step 3 : Finding the next two terms

The next two terms in the sequence will be:

...38 57 80...

+19 +23

So the sequence will be: 5;12;23;38;57;80.

Step 4 : Determine values for a, b and c

2 a = 4

which gives a = 2

And 3a + b = 7

∴ 3(2) + b = 7

b = 7− 6

b = 1

And a + b + c = 5

∴ (2) + (1) + c = 5

c = 5− 3

c = 2

Step 5 : Find the rule by substitution

Tn = ax^2 + bx + c

∴ Tn = 2n^2 + n + 2

Example 2: Quadratic Sequence