This is the Important question based on Arithmetic progression Chapter of R.S Aggarwal book for ICSE & CBSE

Board.

Here you have to find the next term of the Given AP.

This is the Question Number 9 Of Exercise 11 D of RS Aggarwal Solution.

# Write the next term of the AP √2,√8,√18,……

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Given sequence is √2 , √8, √18,…

a1 = √2 ,

a2 = √8 = √ ( 2 × 2 ) ×2 = 2√2

a3 = √18 = √ ( 3 × 3 ) × 2 = 3 √2

First term (a ) = a1 = √2

a2 – a1 = 2√2 – √2 = √2

a3 – a2 = 3√2 – 2√2 = √2

Therefore ,

a2 – a1 = a3 – a2 = √2

Common difference (d) = √2

The given sequence is in A.P .

nth term = an = a + ( n-1 ) d

14th term of the A.P = a4

a4 = a + ( 4 – 1 ) d

= a + 3d

= √2 + 3 × √18

= √2 + 3√2

= 4√2

4th term of the given A.P = 4√2

or

a4 = 4√2