SOLUTION: Determine the number of terms in the following arithmetic sequence: 315, 304, 293, ... , 18.

Question 711986: Determine the number of terms in the following arithmetic sequence: 315, 304, 293, ... , 18.
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Determine the number of terms in the following arithmetic sequence:
315, 304, 293, ... , 18
-----
a = 315
d = 304-315 = -11
----
Solve for "n":
a(n) = a + (n-1)d
----
18 = 315 + (n-1)(-11)
-297 = (n-1)(-11)
n-1 = (-297/-11)
n-1 = 27
n = 28 (# of terms)
=====================
Cheers,
Stan H.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

as you can see, in the following arithmetic sequence, , , , ... , , the difference between each term is (the fixed amount is called the common difference, )

...then next term will be

....and so on, up to

To find any term of an arithmetic sequence use formula:
where is the first term of the sequence,
is the common difference, is the number of the term to find
in your case is given ,, and we found that
...solve for

......plug in given values

......the number of terms

RELATED QUESTIONS
Find the number of terms in the following arithmetic sequence.... (answered by KMST)
Arithmetic Series Question: Determine the number of terms in the following arithmetic... (answered by josgarithmetic,MathTherapy)
the number of terms in the following arithmetic sequence... 3a-5, a+1, 7-a,...,... (answered by mananth)
The number of terms in the arithmetic sequence: 5,18,31,44...161... (answered by josgarithmetic)
In an arithmetic sequence, the sum of the first three terms is 18 and the sum of the... (answered by Theo)
1. Find the 25th term of the arithmetic sequence ‒7, ‒4, ‒1, 2, ... 2.... (answered by MathLover1,greenestamps)
The terms 5 + x, 8, and 1 + 2x are consecutive terms in an arithmetic sequence. Determine (answered by MathLover1,josgarithmetic)
Given the sequence 3;6;9;.....;60. a)Determine the number of terms in the sequence... (answered by greenestamps)
Determine the number of terms in the arithmetic series: a1=10 an=74... (answered by MathLover1)