Question

if the number of term in (1+x)^n be 11, find the 5th term and the value of n​

Answer 1

SOLUTION

GIVEN

$\sf{The \: number \: of \: terms \: in \: \: {(1 + x)}^{n} \: is \: 11}$

TO DETERMINE

• The value of n

• 5 th term

EVALUATION

Here it is given that

$\sf{The \: number \: of \: terms \: in \: \: {(1 + x)}^{n} \: is \: 11}$

We know that

$\sf{The \: number \: of \: terms \: in \: \: {(1 + x)}^{n} \: is \: (n + 1)}$

So by the given condition

n + 1 = 11

∴ n = 10

Hence the required value of n = 10

5 th term

$= \sf{t_5}$

$= \sf{t_{4 + 1}}$

$= \sf{ {}^{10}C_4 \: {x}^{4} }$

$= \sf{ 210 \: {x}^{4} }$

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