DAY 32 AGENDA: Back on Track!! This class registers at 9:55. Media Center --- A – GI (Guthas) Comp Lab C3 --- Gl – N (Roach) Comp Lab C5 --- O – Z (Bennett)

Accel PRecalc Unit #4: Sequences & Series Lesson #3: Finite Geometric Sequences and Series EQ: What is the formula to find the sum of a finite geometric sequence?

Recall: Geometric Sequence --- ordered list of numbers with a common ratio called r Ex 1. Determine if each sequence is geometric. Justify your answer.

Write the explicit formula for finding the nth term of a geometric sequence. an = _________________ Ex 2. Write the explicit formula of the geometric sequence whose initial term is 3 and whose common ratio is 2. Then find the first five terms. an = _________________   a1 = ___ a2 = ___ a3 = ___ a4 = ___ a5 = ___ 3 6 12 24 48

Ex 3. Write the explicit formula of the geometric sequence whose first term is a1 = 20 and has a common ratio of r = 1.05. Then find the 15th term of the sequence. 39.599 an = _________________ a15 = ___

Ex 4. Write the explicit formula of the geometric sequence whose third term is a3 = 64 and whose seventh term is a7 = 16,384. Calculate ratio: 16,384 ÷ 64 = 256 But this ratio is from a3 to a7. Now find a1. an = _________________

Geometric Sequences in Summation Notation Recall: Summation Notation But a geometric sequence is NOT LINEAR. A geometric sequence is EXPONENTIAL.

Ex 5. Use summation to express each sum. HINT: Identify initial term HOW? r = an ÷ an-1 Calculate common ratio. 5 + 15 + 45 + … + 3645 5 15 5 3 a1 = _____ an = ______ an-1 =______ r = ___ r = 15 ÷ 5

How do we find the UPPER LIMIT? RECALL: Solve EXPONENTIALS using LOGS!!

Solve for upper limit using LOGS, but use ¼ NOT -¼. a1 = _____ an = ______ an-1 =______ r = ___ 2 Solve for upper limit using LOGS, but use ¼ NOT -¼. 7 = n Take log of both sides, then divide.

Assignment: p. 644 ODDS #1 - 41

Each consecutive term increases by a factor of r. How to Find the Sum of a Finite Geometric Sequence: Each consecutive term increases by a factor of r.

Solve for Sn

12 (0.3)12 1.2 0.3 4(0.3)1

5 6 2 (2)5 Be careful if the INDEX begins at i = 0. You will need to adjust the summation formula so that it BEGINS AT i = 1. Ex. WHY? For the summation formula, the first term is a1, not a0.

You now know 2 formulas: Summation for an Arithmetic Sequence Summation for a Finite Geometric Sequence These are NOT interchangeable and ONLY work for their SPECIFIC type of sequence.

Assignment: p. 644 ODDS #55 - 67