Accel Precalc Unit 4 Sequences Series Lesson 4

Accel Precalc Unit #4: Sequences & Series Lesson #4: Infinite Geometric Sequences and Series EQ: What is the formula to find the sum of an infinite geometric sequence?

When the ratio is greater than 1, the terms in the sequence will get _______ larger and _______. larger If you add larger and larger numbers forever, you will get ___ ∞ for an answer. So, we don't deal with infinite geometric 1 series when the ratio is greater than ___.

The ratio can't equal 1 ___ because then the series wouldn't be geometric (WHY? ) and 0 the sum formula would have division by ___. The only case left, then, is when the ratio is ______ less than 1.

List the first 10 terms for this sequence. 1 1/32 ½ 1/64 ¼ 1/128 1/256 1/16 1/512 As the sequence goes on, the terms are getting smaller and ____, ____ approaching ____. smaller 0

0 So, if you replace rn with ___ 0 in the summation formula, the 1 - rn part just 1 becomes ____, and the numerator just a 1 becomes ____.

Day 34 Agenda: DG 15 --- 10 minutes

***If |r| > 1, then finding the sum is NOT POSSIBLE!

2. 4 0. 6

0. 01 0. 1 1 3(0. 1)n-1 . 1 0. 001 2 3 . 1 3 0. 1

= 0. 5 + 0. 005 + 0. 0005 + … = 5(0. 1) + 5(0. 001) + 5(0. 0001) + … = 5(0. 1)1 + 5(0. 1)2 + 5(0. 1)3 + 5(0. 1)4 + … OR

= 0. 47 + 0. 000047 + … = 47(0. 01) + 47(0. 000001) + … = 47(0. 01)1 + 47(0. 01)2 + 47(0. 01)3 + … OR

= 0. 1 + 0. 06 + 0. 0006 + … = 0. 1 + 0. 6(0. 1) + 0. 6(0. 001) +… = 0. 1 + 0. 6(0. 1)2 + 0. 6(0. 1)3 +… OR CHECK:

Recall: At --- final amount of money after t P 0 --- initial amount of money; principle r --- annual interest rate (decimal) n --- times per year interest is calculated t --- total number of times interest is calculated

Ex. A deposit is made of $50 on the first day of each month in a savings account that earns 6% compounded monthly. What is the balance of this annuity at the end of 2 years?

Total Balance will be sum of the balances after the 24 deposits. Use the sum formula for a finite geometric series. 24 This is the LAST deposit made. It will earn interest for 1 month. 50(1. 005)1

Ex. A deposit is made of $50 on the first day of each month in a savings account that earns 6% compounded monthly. What is the balance of this annuity at the end of 2 years? This account will have a balance of $1277. 95 at the end of 2 years.

Assignment: p. 645 ODDS #69 – 91