SOLUTION: How many terms of the arithmetic progression 24,22,20 are needed to give the sum of 150?
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Question 796191: How many terms of the arithmetic progression 24,22,20 are needed to give the sum of 150?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
THE MENTAL MATH WAY:
The sum of an arithmetic progression is the average of the first and last terms times the number of therms.
If we add all the numbers between and , we would be adding 12 terms, and multiplying times 12 is not easy.
Leaving out 2, and 4, I would have just 10 terms, and
24+22+20+ ,,, +10+8+6 =
So adding we get 150.
WITH FORMULAS
That progression has a first term
and a common difference
The sum of the first terms of an arithmetic progression can be calculated as
In this case that sum would be 150, so
-->
Adding the 10 terms 24+22+ ... +10+8+6,
or adding the 15 terms 24+22+ ... +10+8+6 +4+2+0-2-4
we get 150,
but I would say terms are needed to get to 150.
There is no need to keep adding 4+2+0+(-2)+(-4)=0.
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