Precalculus Day 8

Unit 1

1)

KNIGHT’S CHARGE

Find three geometric means between 2 and 512.

9/2/15 2) For an arithmetic sequence, 𝑆 14 = 245 and 𝑎 1 = 5 . Find 𝑎 50 .

3) Find the sum of the sequence: 24576, 12288, 6144, 3072, 1536, 768, … , 0.1875

4) Find the sum of the series, if it exists: a. 1 + 5 + 25 + 125 + ⋯ b. 81 − 9 + 3 − 1 + ⋯

Check Homework

Sigma Notation

Write each of the following series in sigma notation:  1 + 5 + 9 + 13 + 17 + 21 + 25  {-18, -13, -8, -3, 2, 7, 12}  {0,2,4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30,…} Sigma Notation

Sigma Notation

Write each of the following series in sigma notation:  {2, 6, 18, 54}  { 2000, 400, 80, 16, 3.2, 0.64

}  {1, 2, 4, 8, 16, 32, 64, 128, … } Sigma Notation

Example: Find the sum.

3 ∙ (−2) 𝑛 Sigma Notation

Example: Write the following series in sigma notation.

 {10, 100, 1000, 10000}  0,8,16, 24, … , 72  1, 4, 9, 16, 25, … , 144 Sigma Notation

BINGO

 Fold a sheet of paper in half FOUR times.



(Think of this as a geometric sequence where

𝑎 1 = 1

and r=2. How many

“squares” should you have after folding a piece of paper 4 times? ) Place one of the following in each of the squares.

195 Diverges 40 1960 2309 Converges 120 91 346 630

Homework