Everything Maths Grade 11

5.2 CHAPTER 5. QUADRATIC SEQUENCES

Extension: Plotting a graph of terms of a quadratic sequence

Plotting Tnvs. n for a quadratic sequence yields a parabolic graph.

Given the quadratic sequence,

3; 6; 10; 15; 21;...

If we plot each of the terms vs. the corresponding index, we obtain a graph of a parabola.

�

�

�

�

�

�

�

�

�

�

Term:

T

n

y-intercept: T 1

1 2 3 4 5 6 7 8 9 10

Index: n

a 1

a 2

a 3

a 4

a 5

a 6

a 7

a 8

a 9

a 10

Chapter 5 End of Chapter Exercises

1. Find the first five terms of the quadratic sequence defined by:

an= n^2 + 2n + 1

2. Determine which ofthe following sequencesis a quadratic sequenceby calculating
   the common second difference:
   (a) 6;9;14;21;30;...
   (b) 1;7;17;31;49;...
   (c) 8;17;32;53;80;...
   (d) 9;26;51;84;125;...
   (e) 2;20;50;92;146;...
   (f) 5;19;41;71;109;...
   (g) 2;6;10;14;18;...