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Question
The next term of the A.P. : `sqrt(6), sqrt(24), sqrt(54)` is ______.
Options
`sqrt(60)`
`sqrt(96)`
`sqrt(72)`
`sqrt(216)`
Solution
The next term of the A.P. : `sqrt(6), sqrt(24), sqrt(54)` is `underlinebb(sqrt(96))`.
Explanation:
Given A.P. is `sqrt(6), sqrt(24), sqrt(54)`
∴ First term (a) = `sqrt(6)`
Common difference (d) = `sqrt(24) - sqrt(6)`
= `sqrt(6 xx 4) - sqrt(6)`
= `2sqrt(6) -sqrt(6)`
= `sqrt(6)`
∴ Fourth term = a4
= a + (4 – 1)d
= `sqrt(6) + 3 xx sqrt(6)`
= `4sqrt(6)`
= `sqrt(16 xx 6)`
= `sqrt(96)`
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