Arithmetic Progression
Algebra
Level
3
An
arithmetic progression
consists of 10 terms.
The sum of all of its terms is 197.5.
The 5th term is 18.
What is the sum of the first 3 terms?
The answer is 22.5.
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1 solution
Assume that the first term is a and the common difference is b. Then the nth term is a+(n-1)b, so 18=a+4b and the sum of the first ten terms is 10a+45b=197.5. Solving these two equations yields a=4 and b=3.5. So the sum of the first three terms is 4+7.5+11=22.5