Question

http://i.imgur.com/Bulb6ue.png

1. The graph shows the first three terms in a geometric sequence.

A. What is the common ratio r? Explain how you determined your answer.
B. What is the recursive formula for the sequence?
C. What is the iterative formula for the sequence?
D. Show how to use your answer from Part C to find the eighth term of the sequence.

Answer 1

for part A :
common ratio = (next term) / (present term)

Answer 2

just take the ratio of 2nd and 1st terms

Answer 3

look at the graph :
first term = ?
second term = ?

Answer 4

First Term: 2
Second term: 5

??

Answer 5

Yes !
common ratio = (second term)/ (first term)
= ?

Answer 6

0.4?

Answer 7

common ratio = (second term)/ (first term)
= 5/2

Answer 8

leave it in fraction form

Answer 9

So the common ratio is 5/2, I can write that down?

Answer 10

Yep !

Answer 11

Awesome, and B? How do I find the recursive formula?

Answer 12

multiplying the common ratio to present term gives u the next term, so the recursive formula is :

\(\large a_{n+1} = a_n \times r = a_n \times \dfrac{5}{2} = \dfrac{5}{2}a_n\)

Answer 13

Great, thank you! And C, D please

Answer 14

for part C, use the general term of geometric sequence formula :
\(\large a_n = a_1r^{n-1}\)

Answer 15

You knw \(\large a_1 = 2\), \(\large r = \dfrac{5}{2}\)

plug them in above formula^

Answer 16

5?

Answer 17

wym 5 ?

Answer 18

2*5/2= 5(x-1) that's my answer for C right?

Answer 19

ahh no, just plug them in the formula, no simplification is possible...

Answer 20

\(\large a_n = 2\left(\dfrac{5}{2}\right)^{n-1} \)

Answer 21

Ah I see, and D?

Answer 22

You cannot cancel 2's cuz the other 2 is under exponent

Answer 23

Yeah now I see, haha took me a bit to understand. And how would I use my answer from C to find the 8th term?

Answer 24

just plugin n = 8 and evaluate

Answer 25

\(\large a_n = 2\left(\dfrac{5}{2}\right)^{n-1} \)

\(\large a_8 = ? \)

Answer 26

Hmm, I don't know.

Answer 27

\(\large a_n = 2\left(\dfrac{5}{2}\right)^{n-1} \)

\(\large a_8 = 2\left(\dfrac{5}{2}\right)^{8-1} = 2\left(\dfrac{5}{2}\right)^{7} \)

Answer 28

use ur calculator

Answer 29

1220.703125

Answer 30

http://www.wolframalpha.com/input/?i=2%285%2F2%29%5E7

Answer 31

1220.703125

Answer 32

looks good^

Answer 33

Awesome thanks! Do you have any more time because I have one more question?

Answer 34

I'll try, ask...

Answer 35

http://i.imgur.com/T0wRI4i.png

The matrices show the number of indoor and outdoor volunteers in different age groups.


A) Create one matrix that shows the total number of indoor and outdoor volunteers in different age
groups. Name the matrix T.

B) What is the value of the element at t11 and what does that value indicate?

C) Create a matrix by subtracting the women’s matrix from the men’s matrix. Name the matrix D.

D) What is the value of the element at d12 and what does that value indicate?

Answer 36

Alright, so the given matrices represent men and women volunteers separately

Answer 37

total number of volunteers = [men volunteers] + [women volunteers]

Answer 38

for part A, just add both the given matrices

Answer 39

you familiar wid matrix addition right ?

Answer 40

A bit, not too well.

Answer 41

So my answer for A should look like this