Question

The first three terms in the expansion of a binomial are 1,10 and 40. Find the expansion.

Answer 1

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Answer 2

Answer:

The expansion is $(1+14)^n$

Step-by-step explanation:

Given : The first three terms in the expansion of a binomial are 1,10 and 40.

To Find : The expansion?

Solution :

Let the expansion be $(a+b)^n$

We have given, First term is

$^nC_0a^nb^0=a^n=1$

So, a=1

Second term is

$^nC_1a^{n-1}b^1=n\times b=10$

So, $nb=10$ ......(1)

Third term is

$^nC_2a^{n-2}b^2=n\times(n-1)\times b^2=40$

So, $n(n-1)b^2=40$ ....(2)

Dividing (1) and (2),

$\frac{n(n-1)b^2}{nb}=\frac{40}{10}$

$(n-1)b=4$

$nb-b=4$

Put the value from (1),

$10-b=4$

$b=14$

So, a=1 and b=14

Therefore, The expansion is $(1+14)^n$