If the coefficient of $2^{n d}$ , $3^{r d}$ & $4^{t h}$ terms in the expansion ${(1 + x)}^{2 n}$ are in A.P., which of the following hold good

n^{2} - 9 n + 7 = 0

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2 n^{2} - 9 n - 7 = 0

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2 n^{2} - 9 n + 7 = 0

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9 n^{2} - 7 n + 2 = 0

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Solution

The correct option is C $2 n^{2} - 9 n + 7 = 0$
Hence
$^{2 n} C_{1}$ , $^{2 n} C_{2}$ and $^{2 n} C_{3}$ are in A.P.
Therefore
It must follow that
$(2 n - 2 (2))^{2} = (2 n + 2)$
$(2 n - 4)^{2} = 2 (n + 1)$
$4 (n - 2)^{2} = 2 (n + 1)$
$2 (n^{2} - 4 n + 8) = n + 1$
$2 n^{2} - 8 n + 8 = n + 1$
$2 n^{2} - 9 n + 7 = 0$

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Similar questions

The coefficients of 2nd, 3rd and 4th terms in the expansion of $(1 + x)^{2 n}$ are in A.P., show that $2 n^{2} - 9 n + 7 = 0.$

2^{n d}

3^{r d}

4^{t h}

(1 + x)^{2 n}

2 n^{2} - 9 n + 7 = 0

2^{n d}, 3^{r d}, 4^{t h}

(1 + x)^{2 n}

A . P

2 n^{2} - 9 n + 8 =

If the coefficients of 2nd, 3rd and 4th terms in the expansion of $(1 + x)^{2 n}$ are in AP, show that $2 n^{2} - 9 n + 7 = 0$

2^{n d}, 3^{r d}

4^{t h}

(1 + x)^{2 n}

A . P

2 n^{2} - 9 n + 7

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