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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 A.P. What is the common difference ?



Answer -

an = a + nb
Let n= 1, 2, 3, 4, 5, тАжтАжтАж.
a1┬а= a + b
a2┬а= a + 2b
a3┬а= a + 3b
a4┬а= a + 4b
a5┬а= a + 5b
We see that it is an A.P. whose common difference is b and a for any real valueof a and b
as a2┬атАУ a1┬а= a + 2b тАУ a тАУ b = b
a3┬атАУ a2┬а= a + 3b тАУ a тАУ 2b = b
a4┬атАУ a3┬а= a + 4b тАУ a тАУ 3b = b
and a5┬атАУ a4┬а= a + 5b тАУ a тАУ 4b = b

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