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The coefficients of three consecutive te...

The coefficients of three consecutive terms in the expansion of `(1 + a)^n` are are in the ratio 1: 7: 42 Find n.

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The correct Answer is:
`5^(th)` and `6^(th)` terms
Let the two successive terms in the expansion of `(1+x)^(24)` be `(r+1)` th and `(r+2)` th terms.
So, `T_(r+1) = .^(24)C_(r )x^(r)`
and `T_(r+2)=.^(24)C_(r+1)x^(r+1)`
Given that, `(.^(24)C_(r))/(.^(24)C_(r+1)) = 1/4`
`rArr (r+1)/(24-(r+1)+1) = 1/4`
`rArr 4r + 4 = 24-r`
`rArr 4r+4 = 24 -r`
`rArr r = 4`
` :. T_(4+1) = T_(5)` and `T_(4+2) = T_(6)`
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