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If the coefficients of a^(r-1), a^(r ), ...

If the coefficients of `a^(r-1), a^(r ), a^(r+1)` in the binomial expansion of `(1 + a)^(n)` are in Arithmetic Progression, prove that: `n^(2) -n(4r+1) + 4r^(2) -2=0`

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If the coefficient of the rth, (r+1)th and (r+2)th terms in the expansion of (1+x)^(n) are in A.P., prove that n^(2) - n(4r +1) + 4r^(2) - 2=0 .

The coefficients of the (r-1)^(th), r^(th) and (r+ 1)^(th) terms in the expansion of (x+1)^(n) are in the ratio 1:3:5 . find n and r.

Knowledge Check

  • In the expansion of (1+x)^(n), T_(r+1) is:

    A
    `C(n, r+1)x^(n-1)`
    B
    `C(n,r)x^( r)`
    C
    `C(n,r)x^(n+1)`
    D
    `C(n,r-1) x^(r+1)`

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