Lesson 4.4 - Pascal's Triangle
In general, the Pascal’s formula is:
tn,r = tn-1,r-1 + tn-1, r
Example 1:
(a) Evaluate t6,2 = t5,1 + t5,2
(b) Find an equivalent expression for t13,3 and evaluate it.
Example 2: The 1st six terms of row 25 of Pascal's triangle are given as 1, 25, 300, 2300, 12650,
53130. Determine the 1st six terms of row 26.
Relationships within Pascal’s Triangle
There are many "nice" patterns within Pascal's Triangle. Here are a few:
1. Row Sums
Pattern:
Example 3:
(a) What is the sum of the eleventh row?
(b) Which row in Pascal’s Triangle has the sum of its terms equal to 32768?
Relationships within Pascal’s Triangle
2. Perfect Squares
Pattern:
Relationships within Pascal’s Triangle
3. Triangular Numbers
Pattern:
Example 4: How many coins are there in a triangle with 8 rows (the 8th equilateral
triangle)?
Homework:
page.251-Q’s#1-7,10(a, b)