## DrPepperx3 2 years ago Medal? can someone help please c:

1. DrPepperx3

Consider the sequence 2, 6, 18, 54 .... Let n= the term number in the sequence Let A(n)= The value of the nth term of the sequence 4. What is the common ratio in the sequence? 5. Complete each statement a. A(1) = 2 = 2*3 b. A(2) = 6 = 2*3 = 2*3 c. A(3) = 18 = 2*3*3 = 2*3 d. A(4) = 54 = 2*3*3*3 = 2*3

2. phi

ratio means put one number over another. Here they want the ratio of the next number of the current number. in other words, for 2 6 they want 6 over 2 or 18 over 6 or 54 over 18 notice they all simplify to the same number (the "common ratio") for 5, put in the exponent (power) on 3 to make the statement true I'll do 5 b. A(2)= 2*3^1 notice that 3 to the power of 1 is 3,

3. DrPepperx3

Im sorry i understand the first part but i dont understand how to figure out the last one >_<

4. DrPepperx3

How did you get the answer?

5. phi

do you know about exponents? a*a = a^2 a*a*a= a^3 (it is a short-hand, because it gets tedious to write out a^10 ) count the number of 3's and that is the exponent. there is one non-obvious answer though: a^0 (anything to the 0 power) is 1 that is not obvious, but that is the rule.

6. DrPepperx3

Ohhhhhhhhh Ok thank you! do you mind helping me with 2 more questions?

7. phi

8. DrPepperx3

A(1) = 2 = 2*3 b. = 2*3^1 A(3) = 18 = 2*3*3 = 2*3 = 2*3*3^2 A(4) = 54 = 2*3*3*3 = 2*3 = 2*3*3*3^3 ?

9. phi

almost, you write 3^2 instead of 3*3 so , for example, A(3)= 2*3*3 you change 3*3 to 3^2 and get 2*3^2 (you don't write both 3*3 and 3^2) for a.) A(1)=2 you can't multiply by 3 or 3*3 or 3*3*3, but you can multiply by 1 and 3^0 is 1, so you can say A(1)= 2*3^0 can you fix A(4) ?

10. DrPepperx3

oh okay i think i get it now 2*3^3

11. phi

yes

12. DrPepperx3

ty! i get it now(: do you mind helping me with these 2? 6. What is the relationship between the exponent of the base 3 and the value of n? 7. Complete the statement: A(n) = 2*3

13. phi

6. What is the relationship between the exponent of the base 3 and the value of n? they want you to see a pattern a. A(1) = 2* 3^0 b. A(2) = 2* 3^1 c. A(3) = 2* 3^2 d. A(4) = 2* 3^3 as you go from A(1) to A(2) up to A(4), how does the answer change? do you notice that the exponent seems related to "n= the term number in the sequence " ? In other words, without working you should be able to write down A(5) 's answer just by following the pattern. for 7. Complete the statement: A(n) = 2*3 they want you to fill in the exponent of the 3. It won't be n, but it will be one less than n.