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If $3$rd, $4$th, $5$th and $6$th terms in the expansion of $(x + a)^n$ be respectively $a$, $b$, $c$ and $d$ then:

$\frac{b^2 - ac}{c^2 - bd}$ = $\frac{5a}{3c}$.

Similarly,

If $6$th, $7$th, $8$th and $9$th terms in the expansion of $(x + a)^n$ be respectively $a$, $b$, $c$ and $d$ then:

$\frac{b^2 - ac}{c^2 - bd}$ = $\frac{4a}{3c}$.

So, Can we say anything in general about $4$ (or more, perhaps) consecutive terms in the binomial expansion?

Nimit
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1 Answers1

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HINT:

By 'term', I think you mean the coefficient of $a^rx^{n-r}$

The $r$th term will be $\binom nr $

In the coefficient of $s$th term is $T_s$

$$\frac{T_{s+1}}{T_s}=\frac{\binom n{s+1}}{\binom ns}=\frac{n! s!(n-s)!}{n!(s+1)!(n-s-1)!}=\frac{n-s}{s+1}$$

lab bhattacharjee
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