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Show that the sequence defined by a(n) ...

Show that the sequence defined by ` a_(n) = m + (2n - 1)` d, where m and d are constants , is an
A.P. Find its common difference .

Text Solution

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Given `a_(n) = m+ (2n - 1)d `
`therefore a_(n-1) = m + (2n - 2 - 1)d = m + (2n - 3)d `
Now , ` a_(n) - a_(n-1) = m + (2n -1) d - {m + (2n - 3)d}`
`= (2n - 1 - 2n + 3 )d `
2d , which is independent of n.
Hence , the given sequence is an A.P. having common difference 2d .
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