Daily Check

1
Daily Check

• Find the first 3 terms of the following sequence
• Write the formula for the following arithmetic
  sequence.
• -2, 1, 4, 7, 10

2
EOCT Practice
Which expression represents the sum of the first
n multiples of 8?

1. 8n
2. 8n2
3. 4n2 4n
4. 8n2 8n

c
3
EOCT Practice
Alex started a business making bracelets. Her
goal is to sell 6 more bracelets each month than
she sold the previous month. If Alex meets her
goal, what is the total number of bracelets she
will sell in the first 12 months?
d

1. 378
2. 426
3. 498
4. 756

4
Math II
UNIT QUESTION How is a geometric sequence like
an exponential function? Standard MM2A2,
MM2A3 Todays Question How is a geometric
sequence like an exponential function? Standard
MM2A3f,g
5
Sequences and Series
6
Geometric Sequences

• In geometric sequences, you multiply by a common
  ratio each time.
• 1, 2, 4, 8, 16, ...
• multiply by 2
• 27, 9, 3, 1, 1/3, ...Divide by 3 which means
  multiply by 1/3

7
Geometric Sequences

• Find the 8th term of the sequence
• 2,6,18,
• Determine the pattern
• Multiply by 3 (known as the common ratio)
• Write the new sequence
• 2,6,18,54,162,486,1458,4374
• So the 8th term is 4374.

8
Geometric Sequences

• Again, use a formula to find large numbers.
•         an a1 (r)n-1

9
Geometric Sequences

• Find the 10th term of the sequence
• 4,8,16,
• an a1 (r)n-1
• a1 4
• r 2
• n 10

10
Geometric Sequences

• an a1 (r)n-1
• a10 4 (2)10-1
• a10 4 (2)9
• a10 4 512
• a10 2048

11
Geometric Sequences

• Find the ninth term of a sequence if
• a3 63 and r -3
• a1 ?
• n 9
• r -3
• a9 ?
• There are 2 unknowns so you must

12
Geometric Sequences

• First find t1.
• Use the sequences formula substituting t3 in for
  tn.  a3 63
• a3 a1 (-3)3-1
• 63 a1 (-3)2
• 63 a1 9
• 7 a1

13
Geometric Sequences

• Now that you know t1, substitute again to find
  tn.
• an a1 (r)n-1
• a9 7 (-3)9-1
• a9 7 (-3)8
• a9 7 6561
• a9 45927

14
Class work

• Coach Book Page 93 and 94

15
Homework

• Page 145 2-16 (even)