Download presentation

1
**12.2 Geometric Sequences and Series**

2
The ration of successive terms in a geometric sequence is a constant called the common ratio, denoted r. Geometric Sequence – a sequence in which each term after the first, a1, is the product of the preceding term and the common ratio, r. a1, a1r, a1r2, …

3
**Ex 1 Find r and the next three terms.**

B. 2t – 10, -4t + 20, 8t – 40, …

4
**Recursive formula for geometric sequences: an = an-1 x rn-1**

The nth term of a geometric sequence is given by: an = a1rn-1

5
**Ex 2 Find the 12th term of -24, 26.4, -29.04, …**

6
**Geometric sequences can model growth or decay.**

For a common ratio greater than 1, a sequence may model growth. (compound interest, population growth, etc.) For a positive common ratio less than 1, a sequence may model decay. (radioactive behavior and depreciation)

7
Ex 3 A new car costing $23,000 depreciates at the rate of 40% per year for four years. Find the value of the car at the end of four years.

8
**Find a sequence that has two geometric means between 128 and 54.**

The terms between any two nonconsecutive terms of a geometric sequence are called geometric means. Find a sequence that has two geometric means between 128 and 54.

9
**A geometric series is the sum of the terms of a geometric sequence.**

10
**Ex 4 find the sum of the first 8 terms of 14 – 70 + 350 – 1750 + …**

11
**Banks use compound interest to determine earnings in accounts or how much to charge for loans.**

12
Ex 5 On April 1 of every year for 25 years, Jim deposits $2000 in an IRA which pays an APR of 10% compounded annually. If he makes no withdrawals, how much will he have in the account at the end of 25 years?

Similar presentations

OK

Aim: Geometric Sequence & Series Course: Alg. 2 & Trig. Do Now: Aim: What are geometric sequences? Annie deposits $1000 in a bank at 8%. interest is compounded.

Aim: Geometric Sequence & Series Course: Alg. 2 & Trig. Do Now: Aim: What are geometric sequences? Annie deposits $1000 in a bank at 8%. interest is compounded.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google