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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:
`sqrt2, sqrt8, sqrt18, sqrt32 ...`
Solution
`sqrt2, sqrt8, sqrt18, sqrt32 ...`
Here,
a2 - a1 = `sqrt8 - sqrt2 = 2sqrt2 - sqrt2 = sqrt2`
a3 - a2 = `sqrt18 - sqrt8 = 3sqrt2 - 2sqrt2 = sqrt2`
a4 - a3 = `4sqrt2 - 3sqrt2 = sqrt2`
⇒ an+1 - an is same every time.
Therefore, `d = sqrt2` and the given numbers are in A.P.
Three more terms are
a5 = `sqrt32 + sqrt2 = 4sqrt2 + sqrt2 = 5sqrt2 = sqrt50`
a6 = `5sqrt2 +sqrt2 = 6sqrt2 = sqrt72`
a7 = `6sqrt2 + sqrt2 = 7sqrt2 = sqrt98`
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