SOLUTION: Find the number of terms in the following arithmetic sequence. 8,11,14,17,...41

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Question 1003573: Find the number of terms in the following arithmetic sequence.
8,11,14,17,...41
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Each term is 3 more than the one before.
11-8=3 , 14-11=3 , etc.

MENTAL MATH:
The difference between the last term an the second term is
41-11=30=3%2A10 .
That means that after 11 , 3 was added 10 times,
meaning that there are 10 terms after 11 .
Since 11 is term number 2 ,
there are 2%2B10=highlight%2812%29 terms.

FORMULA-HAPPY:
Since each term is 3 more that the one before,
the common difference for this arithmetic sequence is d=3 .
The first tern is a%5B1%5D=8 .
In an arithmetic sequence, term number n is
a%5Bn%5D=a%5B1%5D%2B%28n-1%29%2Ad .
In this arithmetic sequence, term number n is
a%5Bn%5D=8%2B3%28n-1%29 .
We want to know what is the term number n for the last term, 41 .
So we write,
8%2B3%28n-1%29=41 , and solve for n :
8%2B3%28n-1%29=41-->3%28n-1%29=41-8-->3%28n-1%29=33-->n-1=33%2F3-->n-1=11-->n=11%2B1-->highlight%28n=12%29 .