In the expansion of (a + b)n, first three terms are 243,810 and 1080 respectively, then the fourth term of the expansion is (n ∈ N)

Question

In the expansion of (a + b)n, first three terms are 243,810 and 1080 respectively, then the fourth term of the expansion is (n ∈ N) (A) 32 (B) 720 (C) 510 (D) 420

Tardigrade Admin · Accepted Answer

T1=an,T2=nan - 1b, T3=(n (n - 1)/2)an - 2⋅ b2 Now, (T22/T1 T3)=(2 n/n - 1)=(810 × 810/243 × 1080)=(5/2) ⇒ n=5 So, a=3 and b=2 , Hence, T4= 5C3⋅ 32⋅ 23=720

Q. In the expansion of $(a + b)^{n},$ first three terms are $243, 810$ and $1080$ respectively, then the fourth term of the expansion is $(n \in N)$

$32$

$720$

$510$

$420$

Q. In the expansion of (a+b)n, first three terms are 243,810 and 1080 respectively, then the fourth term of the expansion is (n∈N)

32

720

510

420

T1​=an,T2​=nan−1b, T3​=2n(n−1)​an−2⋅b2 Now, T1​T3​T22​​=n−12n​=243×1080810×810​=25​ ⇒n=5 So, a=3 and b=2 , Hence, T4​=_5C3​⋅32⋅23=720

Q. In the expansion of $(a + b)^{n},$ first three terms are $243, 810$ and $1080$ respectively, then the fourth term of the expansion is $(n \in N)$

$32$

$720$

$510$

$420$