If the coefficients of the rth term and (r + 1)th term in the expansion of (1 + x)20 are in the ratio 1: 2, then r is equal to

Question

If the coefficients of the rth term and (r + 1)th term in the expansion of (1 + x)20 are in the ratio 1: 2, then r is equal to (A) 6 (B) 7 (C) 8 (D) 9

Tardigrade Admin · Accepted Answer

rth term in the expansion of (1 + x)20 is 20Cr- 1 (x)(r-1) (r + 1)th term in the expansion of (1 + x)20 is 20Cr(x)r Now, (20Cr-1/20Cr) = (1/2) ⇒ (r/21-r) = (1/2) ⇒ 2r = 21 -r ⇒ r = 7.

Q. If the coefficients of the $r^{t h}$ term and $(r + 1)^{t h}$ term in the expansion of $(1 + x)^{20}$ are in the ratio $1 : 2$ , then $r$ is equal to

$6$

$7$

$8$

$9$

Q. If the coefficients of the rth term and (r+1)th term in the expansion of (1+x)20 are in the ratio 1:2, then r is equal to

6

7

8

9

rth term in the expansion of (1+x)20 is 20Cr−1​(x)(r−1) (r+1)th term in the expansion of (1+x)20 is 20Cr​(x)r Now, 20Cr​20Cr−1​​=21​ ⇒21−rr​=21​ ⇒2r=21−r ⇒r=7.

Q. If the coefficients of the $r^{t h}$ term and $(r + 1)^{t h}$ term in the expansion of $(1 + x)^{20}$ are in the ratio $1 : 2$ , then $r$ is equal to

$6$

$7$

$8$

$9$