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Big Ideas Math Algebra 2, 2014

BI

Big Ideas Math Algebra 2, 2014 View details

5. Using Recursive Rules with Sequences

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Exercise 69 Page 450

a First, let's analyze the sequence

T_{n} .

Triangular Numbers

The numbers

T_{n}

are represented by the points of following diagrams.

b Of course, the first triangular number is

T_{1} = 1 .

Notice that the number of dots in

T_{n}

is

n

more than the number of dots in

T_{n - 1} .

Therefore, we can write a recursive rule for

T_{n} .

c Of course

T_{1} = S_{1} .

Now, let's analyze the situation when

n > 1 .

Notice that a square

S_{n}

can be divide into two smaller triangles,

T_{n}

and

T_{n - 1},

as in the following picture.

Subchapter links

Communicate Your Answer p.441

Monitoring Progress p.442-446

Exercises p.447-450