SOLUTION: the number of terms in the following arithmetic sequence... 3a-5, a+1, 7-a,..., 109-35a

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Question 1033214: the number of terms in the following arithmetic sequence...
3a-5, a+1, 7-a,..., 109-35a

Answer by mananth(16946) About Me  (Show Source):
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3a-5, a+1, 7-a,..., 109-35a

first term = 3a-5
d= (a+1)-(3a-5) = -2a+6
tn = 109-35a

109-35a = (3a-5)+(n-1)(-2a+6)
%28114-38a+%29+%2F%28-2a%2B6%29+=+n-1
%2838%283-a%29%29%2F%282%283-a%29%29=n-1
n=20