Question

The next term of the A.P. : `sqrt(6), sqrt(24), sqrt(54)` is ______.

पर्याय

• `sqrt(60)`

• `sqrt(96)`

• `sqrt(72)`

• `sqrt(216)`

Answer 1

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)`