25 Find n and x in the expansion of 1+xn, if the fifth term is four times the - Maths - Binomial Theorem

Question

25 Find n and x in the expansion of 1 + x n , if the fifth term is
four times the fourth term and the fourth term is 6 times the third
term

Neha Sethi · Accepted Answer

Dear student
The general term is given by Tr+1=nCrxn-ryr for x+ynSo, for 1+xnT4+1=nC41n-4x4=nC4x4T3+1=nC31n-3x3=nC3x3A
T
QT4+1=4×T3+1nC4x4=4×nC3x3n! x44!n-4!=4n! x33!n-3!x4!n-4!=43!n-3!x4×3! n-4!=43!n-3×n-4!x4 =4n-3n-3x=16  
1T3+1=nC31n-3x3=nC3x3T2+1=nC21n-2x2=nC2x2and T3+1=6 T2+1nC3x3=6 nC2x2n! x33!n-3!=6 n! x22!n-2!x3!n-3!=6 2!n-2!x3×2! n-3!=6 2!n-2n-3!x3=6 n-2n-2x=18  
2Solving 1 and 2n=11 and x=2
Regards

25. Find n and x in the expansion of 1 + x n , if the fifth term is four times the fourth term and the fourth term is 6 times the third term.

25. Find n and x in the expansion of ${(1 + x)}^{n}$ , if the fifth term is four times the fourth term and the fourth term is 6 times the third term.