Question

No of terms of expansion (x-2y+3z)^n is 45 then n is

Answer 1

Answer:

n = 8

Step-by-step explanation:

We know that number of terms in the expansion of $(x+y)^n$ are $n+1$

Similarly as a general rule, it is worth to remember that the number of terms in the expansion of $(x+y+z)^n$ are

$\frac{(n+1)(n+2)}{2}$

As given in the question

$\frac{(n+1)(n+2)}{2}=45$

$\implies (n+1)(n+2) =45\times 2$

$\implies (n+1)(n+2) =90$

$\implies n^2+3n+2 =90$

$\implies n^2+3n-88 =0$

$\implies n^2+11n-8n-88 =0$

$\implies n(n+11)-8(n+11) =0$

$\implies (n+11)(n-8) =0$

$\implies n=-11, 8$

But n cannot be negative

∴ $n=8$

Hope this helps.

Note: the proof of the number of terms in the expansion of  $(x+y+z)^n$ is a simple one and has not been provided here.