Question

Find numerically the greatest term in the expansion of (3x +2)⁹ where x = 3/2

• A. $\frac{7 \times 3^{13}}{4}$
• B. $\frac{5 \times 3^{13}}{2}$
• C. $\frac{7 \times 3^{13}}{2}$
• D. $\frac{5 \times 3^{12}}{2}$

Answer 1

Answer: (C)

$\frac{7 \times 3^{13}}{2}$

Answer 2

$\frac{(n + 1)| ⥂ |a|}{|x| + |a|}$

= $\frac{(9 + 1)| ⥂ |2|}{|3x| + |2|}$

= $\frac{10 \times 2}{\left| \frac{3 \times 3}{2} \right| + 2}$

= $\frac{40}{13}$¹ integer

i.e. 3 < $\frac{40}{13}$< 4

\ T₄ will be the greatest term.

i.e. T₄ = ⁹C₃ (3x)⁶ (2)³ = $\frac{7 \times 3^{13}}{2}$