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Index of (r+1)th Term from End When Counted from Beginning

If the coeffi...

Question

If the coefficients of rth ,(r + 1)th , and (r + 2)th terms of $(1 + x)^{n}$ are in A.P. then $n^{2} - (4 r - 1) n + 4 r^{2} =$

A

1

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B

2

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C

3

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D

2r

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Solution

The correct option is B
2

the coefficient of (r + 1)th term in $(1 + x)^{n} i s n C_{r}$

Given that $n C_{r - 1}, n C_{r}, n C_{r + 1} a r e i n A . P \Rightarrow 2 n C_{r} = n C_{r - 1} + n C_{r + 1} \Rightarrow n^{2} - (4 r + 1) n + 4 r^{2} = 2$

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