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

Show that the sequence `t_(n)` defined by `t_(n)=5n+4` is AP, also find its common difference.

Text Solution

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We have, `t_(n)=5n+4`
On replacing n by `(n-1)`, we get
`t_(n-1)=5(n-1)+4`
`implies t_(n-1)=5n-1`
`therefore t_n-t_(n-1)=(5n+4)-(5n-1)=5`
Clearly, `t_n-t_(n-1)` is independent of n and is equal to 5. So, the given sequence is an AP with common difference 5.
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