SOLUTION: Find a<sub>n</sub> for the arithmetic series with S<sub>16</sub> = -288, and a<sub>1</sub> = -21

Algebra.Com
Question 1092307: Find an for the arithmetic series
with S16 = -288, and a1 = -21
Found 2 solutions by greenestamps, Edwin McCravy:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The sum of n terms of an arithmetic series is the number of terms, n, multiplied by the average of all the terms. Since the numbers in an arithmetic series are equally spaced, the average of all the terms is the average of the first and last.

If S_16 = -288, then the average of all the terms is -288 divided by 16, which is -18.

If a_1 is -21 and the average of the 16 terms is -18, then the last term a_16 is -15.

a_16 is a_1 plus the common difference 15 times:




The first term is -21 and the common difference is 2/5; the formula for the n-th term is
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!


Substitute n = 16, a1 = -21



Substitute S16 = -288.

 

Now simplify that and solve for d.

When you find d, substitute it and a1 = -21

into 



And simplify the right side:

You finish.

Edwin
RELATED QUESTIONS

Consider an arithmetic series has 14 terms, with t 1 = -100 and t... (answered by stanbon)
Define the a3 and a4 terms of the recurrence relation:... (answered by Edwin McCravy)
let an be an arithmetic sequence. if a4=27 and a9=67,... (answered by Edwin McCravy)
Find the first six terms of the sequence. a1 = -3, an =... (answered by Edwin McCravy)
When the constraint 6x1 + 17x2 < 28 is converted to an... (answered by Edwin McCravy)
determine the number of terms in the arithmetic series... a sub 1 = -27 a sub n =... (answered by ewatrrr)
Find the indicated 25th partial sum of the arithmetic sequence. A#1=100,... (answered by Edwin McCravy)
The sequences are defined using recursion formulas. Write the first four terms of each... (answered by Edwin McCravy)
Consider a sequence 4, x, 9, ... with x>0 If the sequence is geometic, find (a) the... (answered by stanbon)