Sat November 10, 2012 By:

Prove that no matter what the real numbers a and b are, the sequence with nth term a + nb is always an A.P. What is the common difference?

Expert Reply
Sat November 10, 2012
nth term, an=a+nb
n-1 th term, an-1=a+(n-1)b
Differenece of two consecutive terms
= an-an-1= a+nb-a-nb+b = b
which is constant
Hence the sequence is an AP and the common difference is b
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