CHAPTER 5. QUADRATIC SEQUENCES 5.2
1. 3; 6; 10; 15; 21;...
2. 4; 9; 16; 25; 36;...
3. 7; 17; 31; 49; 71;...
4. 2; 10; 26; 50; 82;...
5. 31; 30; 27; 22; 15;...
Calculate the common second difference for each of the above examples.
More practice video solutions or help at http://www.everythingmaths.co.za(1.-5.) 01zmGeneral Case
If the sequence is quadratic, the nthterm should be Tn= an^2 + bn + c
T ERMS a + b + c 4 a + 2b + c 9 a + 3b + c 16 a + 4b + c1 stdifference 3 a + b 5 a + b 7 a + b2 nddifference 2 a 2 aIn each case, the seconddifference is 2 a. This fact can be used to find a, then b then c.
Example 1: Quadratic sequence
QUESTIONWrite down the next twoterms and find a formulafor the nthterm of the sequence5;12;23;38;...SOLUTIONStep 1 : Find the first differences between the terms5 12 23 38
+7 +11 + 15
i.e. 7;11;15.