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

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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.

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  1. 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

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