Hi! I have a question! I forgot how to do these two problems, and I need some help in solving them! Thanks so much!
1.) Find the first 5 terms of the sequence given by a1=2, an=3an-1 -1.
(It's: a sub 1 =2, a sub n= 3a sub n-1 -1)
Does that make sense?
If not, that's ok. I'll to clarify more if it's still strange (which it is, I know!)
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!