Question

I don't quite get this. Fan and medal!

Answer 1

Part 2: Create a scenario for a geometric sequence. For example, Anthony goes to the gym for ______ minutes on Monday. Every day he _________his gym time by ____________. If he continues this pattern, how many minutes will he spend at the gym on the 5th day? Be sure to fill in the blanks with the words that will create a geometric sequence. Use your scenario to write the formula for the 5th term in your sequence using sequence notation.

Part 3: Use your scenario from part 2 to write a question that will lead to using the geometric series formula. Use the formula to solve for Sn in your scenario.

Answer 2

I've got that he goes for 10 minutes on Monday, and increases by 10% each day.

Answer 3

But how would I write the formula?

Answer 4

10, 10*1.1, The previous number *1.1, The previous number *1.1

Answer 5

Which is the same as:
10, 10*1.1, 10*1.1 *1.1, 10 *1.1 *1.1 *1.1

Answer 6

10, 11, 12.1, 13.31, 14.641

Answer 7

Good so you just told me:
a1 = 10
a2 = 11
a3 = 12.1
a4 = 14.641
...

Answer 8

Now we want to represent that sequence in terms of "n" and "a1"

Answer 9

a4 = 13.31, 15 = 14.641

Answer 10

*a5

Answer 11

yes yes

Answer 12

we use the formula:
an = a1 * r ^(n-1)

Answer 13

a1 is definitely 10
r is the number you multiply by each time

Answer 14

so 10*1.1^(n-1)

Answer 15

yep make sure to check it... try plugging in a5

Answer 16

14.642*1.1^(n-1)

Answer 17

nope check it out:
an = 10 * 1.1 ^ (n-1)

Well what happens when "n" is actually "5"

Answer 18

(change all n's to 5's)

Answer 19

10*1.1^(14.641-1)