If the coefficients of three consecutive terms in the expansion of are in the ratio 1:5:20, then the coefficient of the fourth term is [2023]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
If the coefficients of three consecutive terms in the expansion of ${(1 + x)}^{n}$ are in the ratio 1:5:20, then the coefficient of the fourth term is [2023]

1 1827

2 5481

3 2436

4 3654

Ans.
(4)

Given, coefficients of three consecutive terms are in the ratio 1 : 5 : 20

$i.e., {}^{n}{C_{r - 1}} : {}^{n}{C_{r}} : {}^{n}{C_{r + 1}} = 1 : 5 : 20$

Now, $\frac{{}^{n}{C_{r - 1}}}{{}^{n}{C_{r}}} = \frac{1}{5} \Rightarrow n = 6 r - 1 ...(i)$

Also, $\frac{{}^{n}{C_{r}}}{{}^{n}{C_{r + 1}}} = \frac{5}{20} \Rightarrow n = 5 r + 4 ...(ii)$

From (i) and (ii), we get

$6 r - 1 = 5 r + 4 \Rightarrow r = 5 \Rightarrow n = 25 + 4 = 29$

$∴$ $The coefficient of 4th term = {}^{29}{C_{3}} = 3654$

Want Us to Email you About Special Offers & Updates?