Question 953582
i believe this is an arithmetic progression.
the formula for the sum of an arithmetic progression is:
Sn = n*(A1+An)/2
For example:
If you have the arithmetic progression 1,2,3,4,5, then the sum is 15.
The formula would be:
Sn = 5 * (1 + 5)/2 = 5 * 6/2 = 5 * 3 = 15.
The formula will get you the sum without all the tears.
Sometimes you have to find An first.
The formula for that is:
An = A1 + (n-1) * d
d is the common difference.
In case you didn't figure it out by now:
A1 is the first term in the series.
An is the nth term in the series.
n is the number of terms in the series.


Let's apply these formulas to your problem:
Your first row is 22 seats, so A1 = 22.
Each succeeding row has 1 more seat, so d = 1.
There are 40 rows in all, so n = 40


First we have to find An.
Then we can find Sn.


An = A1 + (n-1) * d.
replace A1 with 22 n with 40 and d with 1 and the formula becomes:
An = 22 + 39 * 1 = 22 + 39 = 61.


Sn = n * (A1 + An) / 2.
replace n with 40 and A1 with 22 and An with 61 and the formula becomes:
Sn = 40 * (22 + 61) / 2 = 40 * 83/2 = 40 * 41.5 = 1660


You got the right answer.
The sum is 1660.
The formulas, if you remember them, make the job a lot easiwer.


The formulas are, once again:


An = A1 * (n-1)*d


Sn = n * (A1 + An) / 2


Here's some good links for future reference:


<a href = "http://www.regentsprep.org/regents/math/algtrig/atp2/arithseq.htm" target = "_blank">http://www.regentsprep.org/regents/math/algtrig/atp2/arithseq.htm</a>


<a href = "http://www.regentsprep.org/regents/math/algtrig/atp2/geoseq.htm" target = "_blank">http://www.regentsprep.org/regents/math/algtrig/atp2/geoseq.htm</a>