1. NUMBER PATTERN FORMULAS BY::NIKHIL

6. A Closer look at Square number sequence… Let’s consider another set of square number. 400 , 441 , 484 , 529 …. It’s actually 20 2 , 21 2 , 22 2 , 23 2 …. Can be written as ( 1 +19) 2 , ( 2 +19) 2 , ( 3 +19) 2 , ( 4 +19) 2 .. We can replace the nos. in red with ‘n’, giving the formula: (n+19) 2 So the next (5 th ) number would be: (5+19) 2 = 576

7. Arithmetic Sequence Arithmetic sequence is a repetitive ADDITION of a fixed number to give the result. For example, 1 , 3 , 5 , 7 , … We know the next number ( 5 th number) would be 7+2 which is 9. But, what will be, say, the 10 th number? +2 +2 +2 +2 1st 2 nd 3 rd 4 th 5 th

9. Arithmetic Sequence: Exhibit 2 Let’s look at another arithmetic sequence… 10, 15, 20, 25… If we replace the number position with ‘ n’ , we get a formula 5n+5 Using the formula, the value of the 10th number is: 5X10+5 = 55 Checking, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 X 5 + 5 X 5 + 5 X 5 + 5 X 5 + 5 Number position Value of the number 1 10 2 15 3 20 4 25

11. Testing the formula From Exhibit 1: 1, 3, 5, 7,……… 19 Let’s use the formula and test if the 10th number in this arithmetic sequence is 19 a+d(n-1) = 1+2(10-1) =19 From Exhibit 2: 10, 15, 20, 25…… 55 Let’s use the formula and test if the 10th number in this arithmetic sequence is 55 a+d(n-1) = 10+5(10-1) =55

12. Geometric Sequence Geometric sequence is a repetitive MULTIPLICATION of a fixed number to give the result. For example, 5 , 10 , 20 , 40 , … We know the next number ( 5th number) would be 40x2 which is 80. But, what will be, say, the 10th number? 1st 2 nd 3 rd 4 th 5 th x2 x2 x2 x2

13. Geometric Sequence Let’s consider the geometric sequence, 6, 12, 24, 48… X2 X2 X2 If we notice, 6 is the first number ‘ a ’, 2 is the common multiplication ‘ r ’ FORMULA FOR ANY GEOMETRIC SEQUENCE: a x (r) n-1 No. position Value of no. Breakdown 1 6 6x2 0 6x(2) 1-1 2 12 6X2 1 6X(2) 2-1 3 24 6X2 2 6X(2) 3-1 4 48 6X2 3 6X(2) 4-1 We can write, 6x(2) n-1

18. POP QUIZ

19. BIBLIOGRAPHY