# If second, third and fourth terms in the expansion of $(x+a)^{n}$ are 240, 720 and 1080 respectively then the value of n is Option 1) 15 Option 2) 20 Option 3) 10 Option 4) 5

As we learnt in

Properties of Binomial Theorem -

$\dpi{120} ^{n}c_{r}= \frac{n}{r}\: ^{n-1}c_{r-1}= \frac{n}{r}\cdot \frac{n-1}{r-1}\; \; ^{n-2}c_{r-2}\: and \: so\ on...$

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$T_{2}=240;T_{3}=720;T_{4}=1080;\\\\*\frac{720}{240}=\frac{\left ( n-1 \right )}{2}\times \frac{a}{x}\\\\*\left ( n-1 \right )\times \frac{a}{x}=6\\\\*\frac{1080}{720}=\frac{3}{2}=\frac{(n-2)}{3}\times \frac{a}{x}\\\\*\frac{9}{2}=\left ( n-2 \right )\times \frac{a}{x}\\*\frac{(9)}{2\left ( n-2 \right )}=\frac{6}{n-1}\\\\*9n-9=6\times 2\left ( n-2 \right )\\\\*3n=15= > n=5$

Option 1)

15

Incorrect

Option 2)

20

Incorrect

Option 3)

10

Incorrect

Option 4)

5

Correct

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