SOLUTION: in a certain ap the 32nd term is twice the 12th term prove that 70th term is twice the 31st term

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Question 1019525: in a certain ap the 32nd term is twice the 12th term prove that 70th term is twice the 31st term
Answer by robertb(5830) About Me  (Show Source):
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The usual formula for the nth term of an AP is a%5Bn%5D+=+a%5B1%5D+%2B+%28n-1%29d. For the purpose of proving the statement, we use the alternative formula
a%5Bn%5D+=+a%5Bk%5D+%2B+%28n-k%29d, where k = 1, 2, 3, ...., n-1.
We are also given that a%5B32%5D+=+2a%5B12%5D
Using this formula,
a%5B70%5D+=+a%5B32%5D%2B38d+=+2a%5B12%5D+%2B38d+=+2%28a%5B12%5D%2B19d%29+=+2a%5B31%5D,
and the statement is proved.