The numerically greatest term in the expansion of (3 + 2x)^ 44, when x = 1/ 5 is

Question

The numerically greatest term in the expansion of (3 + 2x)⁴⁴, when  x = \(\frac{1}{5}\) is 

(a) 4th term 

(b) 5th term 

(c) 6th term 

(d) 7th term

Answer 1

Answer : (c) 6th term

The general term in the expansion of (3 + 2x) ⁴⁴ is 

T_{r + 1} = ⁴⁴C_r (3)^{44 – r} (2x)^r 

∴ T_r = ⁴⁴C_{r – 1} (3)^{44 – (r–1)} (2x)^r–1 = ⁴⁴C_{r – 1} 3^{45– r} (2x)^r–1

For T_{r + 1} to be the greatest term, \(( where\, x = \frac{1}{5})\) 

⇒ T₆, i.e., the 6th term is numerically the greatest term