SOLUTION: An Arithmetic Sequence has ten terms. The sum of the first three terms is 18 while the sum of the last three terms is 81. What is the sum of all ten terms?
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Question 1083559: An Arithmetic Sequence has ten terms. The sum of the first three terms is 18 while the sum of the last three terms is 81. What is the sum of all ten terms? Answer by ikleyn(52781) (Show Source):
Then the second term is = 6, while the 9-th term is = 27 (why ?)
In other words,
= 6 = , (1)
= 27 = . (2)
Subtract (1) from (2) (both sides). You will get
7d = 27 - 6 = 21 ---> d = = 3.
Hence, = 6 - 3 = 3. Also, = 27+3 = 30.
Now, the sum of 10 terms is = = = 33*5 = 165.
