SOLUTION: I am having trouble understanding this problem. I am supposed to show steps and not have a decimal answer. -17/4 is the ___ term of 2 1/4, 2, 1 3/4 ? Thank you in advance.

Algebra ->  Sequences-and-series -> SOLUTION: I am having trouble understanding this problem. I am supposed to show steps and not have a decimal answer. -17/4 is the ___ term of 2 1/4, 2, 1 3/4 ? Thank you in advance.      Log On


   

Question 1115602: I am having trouble understanding this problem. I am supposed to show steps and not have a decimal answer.
-17/4 is the ___ term of 2 1/4, 2, 1 3/4 ?
Thank you in advance.
Found 2 solutions by MathLover1, Alan3354:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

your sequence is
2+1%2F4,+2, 1+3%2F4,........,-17%2F4
or
+9%2F4,+2, 7%2F4,..........,-17%2F4

first find common difference d
d=2-9%2F4=8%2F4-9%2F4=-1%2F4

so, d=+-1%2F4
first term a%5B1%5D=9%2F4
nth term =>a%5Bn%5D=+-17%2F4
a%5Bn%5D=a%5B1%5D%2B%28n-1%29d
-17%2F4=9%2F4%2B%28n-1%29%28-1%2F4%29
-17%2F4=9%2F4-%28n-1%29%2F4%29
-17%2F4=%289-%28n-1%29%29%2F4%29
-17%2F4=%289-n%2B1%29%2F4%29
-17%2F4+=+%2810+-+n%29%2F4...since denominators same, we have
-17+=+10+-+n
n=10%2B17
n=27
-17%2F4 is the _27th__ term of 2+1%2F4, 2,+1+3%2F4,...


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I am having trouble understanding this problem. I am supposed to show steps and not have a decimal answer.
-17/4 is the ___ term of 2 1/4, 2, 1 3/4 ?
----------
Mixed numbers are useless.
-17/4 is the ___ term of 9/4, 8/4, 7/4 ?
Notice each term is 1/4 less than the preceding term.
From 9/4 to -17/4 would be 26 "steps"
Calling 9/4 term #1 --> the 27th term.