Find the 7th term in the expansion of (3×2 – 1/x3)10.

Answer:

Consider,

7^th term as T₇

T₇ = T₆₊₁

T₇ = ¹⁰C₆ (3x²)^10-6 (-1/x³)⁶

T₇ = ¹⁰C₆ (3)⁴ (x)⁸ (1/x¹⁸)

T₇ = [10×9×8×7×81] / [4×3×2×x¹⁰]

T₇ = 17010 / x¹⁰

∴ 7^th term of the expression (3x² – 1/x³)¹⁰ = 17010 / x¹⁰.