Question

Numerically greatest term, in the expansion of (8–5x)¹⁸ ; is (where x = 2/5)

• A. 1632 × 2²⁴
• B. 1632 × 2²²
• C. 1632 × 2²³
• D. None of these

Answer 1

Answer: (B)

1632 × 2²²

Answer 2

Numerically greatest term in the expansion of

(8 – 5x)¹⁸

= Numerically greatest term in the expansion of (8 + 5x)¹⁸

Now, $\frac{(18 + 1) \times 5x}{8 + 5x}$= $\frac{19 \times 5 \times 2/5}{8 + 5 \times 2/5}$= $\frac{38}{10}$= 3.8

\ Greatest term is t₃₊₁ = ¹⁸C₃ 8³ × $\left( 5 \times \frac{2}{5} \right)^{15}$

= $\frac{18 \times 17 \times 16}{3 \times 2}$× 2⁹⁺¹⁵ = 816 × 2²⁴ = 1632 × 2²³

\ (2) is correct.