SOLUTION: Find the 100th term of a certain arithmetic sequence, given that the 7th term is 16 and the 61st term is 232.

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Question 46737: Find the 100th term of a certain arithmetic sequence, given that the 7th term is 16 and the 61st term is 232.
Answer by adamchapman(301) About Me  (Show Source):
You can put this solution on YOUR website!
You can find the value of the nth term in an arithmetic sequence using the formula u%5Bn%5D=a%2B%28n-1%29d
Where u%5Bn%5D is the nth term,
a = the value of the first term,
d = the difference between two consecutive terms.
Let's look at the 7th term:
u%5B7%5D=a%2B6d=16.............1
Mow the 61st term:
u%5B61%5D=a%2B60d=232...........2
Solve equations (1) and (2) to find a and d.
Multiply equation (1) by 10:
10a%2B60d=160.............3
subtract (2) from (3):
9a=160-232=-72
a=-72%2F9
a=-8................4
Now plug a=-8 into equation 1:
-8%2B60d=160
60d=168
d=2.8
Now we know a and d, we can use the formaula to find the 100th term.
u%5B100%5D=-8%2B99%282.8%29=269.2
I hope this helps,
Adam
P.S. please visit my website, it may be helpful to you. The address is www.geocities.com/quibowibbler