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, 32, 720, 510, 420

MARKS App · Accepted Answer

T 1 = a n , T 2 = n a n - 1 b , T 3 = n n - 1 2 a n - 2 ⋅ b 2 Now, T 2 2 T 1 T 3 = 2 n n - 1 = 810 × 810 243 × 1080 = 5 2 ⇒ n = 5 So, a = 3 and b = 2 , Hence, T 4 = C 5 3 ⋅ 3 2 ⋅ 2 3 = 720

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