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nth Term of A.P

Check whether...

Question

Check whether the following form an AP?
1, 1, 1, 1, ............
Justify your answer, If AP then enter $1$ and if not then enter $0$ .

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Solution

Compare the given series with $a_{1}, a_{2}, a_{3} . . . . . .$ , we get
$a_{2} - a_{1} = 1 - 1 = 0$
$a_{3} - a_{2} = 1 - 1 = 0$
$a_{4} - a_{3} = 1 - 1 = 0$
This shows that the difference of a term and preceding term is always same.
Hence, the given sequence forms an A.P.

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