Hi! I have a question! I forgot how to do these two problems, and I need some help in solving them! Thanks so much!

asub1 = 2 is the first term

asubn can be calculated fron asubn-1, using the formula you prodided
asubn = 3 asubn-1 -1

Thus a sub2 = 3 asub1 - 1 = 5
asub3 = 3 asub2 -1 = 14
asub4 = 3 asub3 -1 = 41
asub5 = ?

Okay!! I think I got it!!! Thank you so much! I'm gonna solve the 5 terms, and write them up here! :) Tell me how I did!

Okay:

a sub1=2
a sub2= 3(2)-1=5
a sub3= 3(5)-1=14
a sub4= 3(14)-1=41
a sub5= 3(41)-1=122

I think that's it! Thanks so much again!

Looks good to me!

It's interestng that the differences between adjacent terms are powers of 3:
3,9,27,81 etc

The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 18 HCF of water is $33.44 , and the cost for using 35 HCF is $61.49. What is the cost for using 27 HCF of water?

Hi! I can help you with that math problem. To find the first 5 terms of the sequence, you need to use the given formula:

a1 = 2, an = 3an-1 - 1

To find the second term, you substitute n = 2 into the formula:

a2 = 3a2-1 - 1

Since a2-1 is equal to a1, you can replace it with 2:

a2 = 3a1 - 1
a2 = 3(2) - 1
a2 = 6 - 1
a2 = 5

So the second term (a2) is equal to 5.

To find the third term, you substitute n = 3 into the formula:

a3 = 3a3-1 - 1

Again, replace a3-1 with a2 (which is equal to 5):

a3 = 3a2 - 1
a3 = 3(5) - 1
a3 = 15 - 1
a3 = 14

So the third term (a3) is equal to 14.

You can continue this process to find the fourth and fifth terms. Let me know if you need help with that too!