SOLUTION: The 4th term of an AP is 27 and the sum of the first and fourth term is 42, what is the third term?

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Question 1083646: The 4th term of an AP is 27 and the sum of the first and fourth term is 42, what is the third term?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
a%5B4%5D=27
a%5B1%5D%2Ba%5B4%5D=42
a%5B1%5D=42-a%5B4%5D
a%5B1%5D=42-27
a%5B1%5D=15
find common difference using formula below:
a%5Bn%5D+=+a%5B1%5D+%2B+d%28n-1%29
a%5B4%5D+=+a%5B1%5D+%2B+d%284-1%29
27=+15%2B+d%283%29
27-15=3d
3d=12
d=4
so, terms are:
a%5B1%5D=15
a%5B2%5D=15%2B4=19
a%5B3%5D=19%2B4=23-> your answer
a%5B4%5D=23%2B4=27