Aim: What are geometric sequences and series?

Aim: Infinite Geometric Sequence/Series Course: Math Literacy

Do Now:

Aim: What are geometric sequences and series?

Find the sum of 12

1

4 0.3n

n

a1 = 4(0.3)1 = 1.2 n = 12r = 0.3

12

1 2 3 12

1

4 0.3 4 0.3 4 0.3 4 0.3 4 0.3n

n L

1

1

1

nrS a

r

121 0.31.2

1 0.3S

1.714

Aim: Infinite Geometric Sequence/Series Course: Math Literacy

The Sum of a Infinite Geometric Sequence

Find the sum of 1

4 0.3n

n

a1 = 4(0.3)1 = 1.2 n = 12r = 0.3

1 2 3 12

1

4 0.3 4 0.3 4 0.3 4 0.3 4 0.3n

n

L

1

1

1

nrS a

r

1 0.31.2

1 0.3S

= ?

Aim: Infinite Geometric Sequence/Series Course: Math Literacy

1

1

4(0.6)n

n

Find

= 4 + 4(0.6) + 4(0.6)2 + 4(0.6)3 + . .

The Sum of a Infinite Geometric Sequence

If |r| < 1, then the infinite geometric sequence a1, a1r2, a1r3, a1r4, . . . . a1rn - 1 . . . has the sum

11

1

n

nS a r

1

1

44(0.6) 10

1 0.6n

n

S

a1 = 4 and r = 0.6 - (|r| < 1)

1

1

a

r

Aim: Infinite Geometric Sequence/Series Course: Math Literacy

Model Problem

Find the sum of 3 + 0.3 + 0.03 + 0.003 + . . .

r

araS n

n

1

11

11

1

1

aS

r

a1 = 3 and r = ?0.1

3 + 3(0.1) + 3(0.1)2 + 3(0.1)3 + . . .

3

1 (0.1)

3

0.9

13

3

Aim: Infinite Geometric Sequence/Series Course: Math Literacy

Model Problems

Find the sum of the series.

160 + 80 + 40 + . . . , n = 6

Find the sum of the infinite series.

160 + 80 + 40 + . . . .

Aim: Infinite Geometric Sequence/Series Course: Math Literacy

Model Problems

Find the sum of the geometric series.

2 3

3 1, , 5

8 4a a n

Aim: Infinite Geometric Sequence/Series Course: Math Literacy

Model Problems

Express the series in sigma notation and find the sum.

54 + 18 + 6 + 2 + 2/3 + 2/9

Aim: Infinite Geometric Sequence/Series Course: Math Literacy

Model Problems

Find a1.

Sn = -55, r = -2/3, n = 5

Aim: Infinite Geometric Sequence/Series Course: Math Literacy

Model Problems

Find the nth term of the geometric sequence.

a2 = -18; a5 = 2/3; n = 6

Aim: Infinite Geometric Sequence/Series Course: Math Literacy

Do Now:

Aim: What are geometric sequences?

Find the nth term of the geometric sequence.

a2 = -18; a5 = 2/3; n = 6