SOLUTION: How many terms are there in the A.P. -7,-4,-1,2...., 101?

Question 983064: How many terms are there in the A.P. -7,-4,-1,2...., 101?
Found 3 solutions by htmentor, Boreal, ikleyn:
Answer by htmentor(1343)   (Show Source): You can put this solution on YOUR website!
The n-th term of an arithmetic progression can be written a_n = a_1 + (n-1)d,
where a_1 = the first term and d = the common difference.
In this case a_1 = -7, and d = 3
For the last term in the sequence we can write 101 = -7 + 3(n-1)
Solve for n:
101 = 3n - 10
n = 111/3 = 37
So there are 37 terms in the sequence.
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
This is an arithmetic series with +3 being the common factor.
There is a difference of 108 between 101 and -7
That divided by 3=36.
The first term is added, so there are 37 terms.
-7,-4,-2 are the three negative ones.
2,5,8,11,14,17,20 are 7 terms.
23 to 50 are 10 more
53 to 80 are 10 more
83,86,89,92,95,98,101 are the last 7
Those are the 37 terms.
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!

The number of terms in this arithmetic progression is

+ = + = 36 + 1 = 37.

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