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The coefficients of three consecutive te...

The coefficients of three consecutive terms of `(1+x)^(n+5)` are in the ratio 5:10:14. Then `n=` ___________.

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Let `T_(r-1), T_(r), T_(r+1)` are three consecutive term of `(1+x)^(n+5)`
`T_(r-1) = .^(n+5)C_(r-2) (x)^(r-2), T_(r) = .^(n+5)C_(r-1)x^(r-1),T_(r+1)=.^(n+5)C_(r)x^(r)`,
where `.^(n+5)C_(r-20)`: `.^(n+5)C_(r-1)` : `.^(n+5)C_(r) = 5 : 10 : 14`.
So, `(.^(n+5)C_(r-2))/(5)= (.^(n+5)C_(r-1))/(10) = (.^(n+5)C_(r))/(14)`
Comparing first two results we have `n - 3r = -9 " "(1)`
Corrparing last two results we have `5n - 12r = -30 " "(2)`
From equation (1) and (2), `n = 6`
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