1. Warm-up Problems
Consider the arithmetic sequence whose first two terms are 3 and 7.
Find an expression for an.
Find the value of a57.
Find the sum of the first 28 terms.

2. Geometric Sequences and Series
A sequence is geometric if the quotient of two consecutive terms is the same.
for any positive integer n
The number r is called the common ratio 2 2 2

3. Ex. Find the first 4 terms of the geometric sequence.
a) an = 2n
b) an = 4(3n) c)
d) an = n2

4. To find the nth term of a geometric sequence, we use the formula
an = a1rn – 1
where a1 is the first term and r is the common ratio
Ex. Find the nth term of the sequence
3, 6, 12, 24, 48,...

5. Ex. Write the 15th term of the geometric sequence whose 1st term is 20 and whose common ratio is 1.05.

6. Ex. Write the 12th term of the geometric sequence 5, 15, 45,...

7. Ex. The 4th term of a geometric sequence is 125 and the 10th term is
Ex. The 4th term of a geometric sequence is 125 and the 10th term is Find the 14th term.

8. To find the sum of finite geometric sequence with n terms, we use the formula
Ex. Find the sum

9. It is possible to take the sum of an infinite geometric sequence and get a finite answer.
Consider
We say that this geometric series converges
A geometric series will converge if |r| < 1, and the sum is given by the formula

10. Ex. Find the sum a) b)

11. Ex. A deposit of $50 is made on the first day of every month in an account that pays 6% compounded monthly. What is the balance at the end of 2 years?

12. Arithmetic
Geometric

13. Practice Problems
Section 8.3
Problems 1, 11, 27, 35, 41, 57, 79, 107