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Question
Following are APs or not? If they form an A.P. find the common difference d and write three more terms:
`3, 3 + sqrt2, 3 + 2sqrt2, 3 + 3sqrt2`
Solution
`3, 3 + sqrt2, 3 + 2sqrt2, 3 + 3sqrt2`
Here,
a2 - a1 = `3 + sqrt2 - 3 = sqrt2`
a3 - a2 = `(3 + 2sqrt2) - (3 + sqrt2) = sqrt2`
a4 - a3 = `(3 + 3sqrt2) - (3 + 2sqrt2) = sqrt2`
⇒ an+1 - an is same every time.
Therefore, `d = sqrt2` and the given numbers are in A.P.
Three more terms are
a5 = `(3 + sqrt2) + sqrt2 = 3 + 4sqrt2`
a6 = `(3 + 4sqrt2) + sqrt2 = 3 + 5sqrt2`
a7 = `(3 + 5sqrt2) + sqrt2 = 3 + 6sqrt2`
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