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Question
Prove that no matter what the real numbers a and b are, the sequence with nth term a+NB is always an AP. What is the common difference?
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Solution
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
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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