Question

Find the next two term of the AP: √3, √12, √27, √48,-​

Answer 1

Answer:

next two term of the ap =√48

Answer 2

Step-by-step explanation:

$given \\ \sqrt{3} \: \: \sqrt{12} \: \: \sqrt{27} \: \: \sqrt{48} \: \: are \: in \: ap \\ a = \sqrt{3} \: \: \: \: \: \: \: \: \: \: \: \: \: d = \ \sqrt{12} - \sqrt{3} = 2 \sqrt{3} - \sqrt{3} \\ \: \: \: \: \: \: = \sqrt{3} \\ we \: know \: that \: \\ an = a + (n - 1)d \\ a5 = \sqrt{3} +( 5 - 1) \sqrt{3} \\ = \sqrt{3} + 4 \sqrt{3} \\ = 5 \sqrt{3} = \sqrt{ {5}^{2} \times 3 } = \sqrt{25 \times 3} = \sqrt{75} \\ a6 = a5 + d \\ = \sqrt{75} + \sqrt{3} = 5 \sqrt{3} + \sqrt{3} = 6 \sqrt{3} = \sqrt{ {6}^{2} \times 3} \\ \: \: \: \: \: \: \: \: \: = \sqrt{36 \times 3} = \sqrt{108} \\ therefore \: a5 = \sqrt{75} \\ \: \: \: \: \: \: \: \: \: a6 = \sqrt{108}$