SOLUTION: Consider the sequence 24, 23 1\4, 22 1/2, ... which term of the sequence is -36

Algebra ->  Sequences-and-series -> SOLUTION: Consider the sequence 24, 23 1\4, 22 1/2, ... which term of the sequence is -36      Log On


   

Question 1161495: Consider the sequence 24, 23 1\4, 22 1/2, ...
which term of the sequence is -36
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
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24, 23%261%2F4, 22%261%2F2, ...
which term of the sequence is -36
first find common difference:
23%261%2F4-24=-3%2F4
23%261%2F4-3%2F4=22%265%2F4-3%2F4=22%262%2F4=22%261%2F2->true
so, this is an arithmetic sequence and common difference is d=-3%2F4
nth term formula is:
a%5Bn%5D=a%5B1%5D%2Bd%28n-1%29.....plug in a%5B1%5D=24 and d=-3%2F4
a%5Bn%5D=24-%283%2F4%29%28n-1%29
to find which term of the sequence is -36, plug in a%5Bn%5D=-36 and solve for n
-36=24-%283%2F4%29%28n-1%29
-36-24=-%283%2F4%29%28n-1%29

-60=-%283%2F4%29%28n-1%29

-60%2F%28-3%2F4%29=n-1.....simplify

20%2F%281%2F4%29=n-1
20%2A4=n-1
80=n-1
n=80%2B1
n=81

so, 81st term of the sequence is -36



Answer by ikleyn(52771) About Me  (Show Source):
You can put this solution on YOUR website!
.

            I want to show you the way to solve the problem in a few lines. 


It is arithmetic progression with the common difference of - 3%2F4.


The distance from the first term of 24 to the last term of -36 is 60 units on the number line.


There are  60%2F%28%283%2F4%29%29 = 20*4 = 80 gaps between the first and the last terms.


Hence, -36 is the 81-th term of the progression.    ANSWER

Solved.