Question

The two consecutive terms in the expansion of ${(3x+2)}^{74}$, whose coefficient are equal, are

• A. $20thand21st$
• B. $30thand31st$
• C. $40thand41st$
• D. $Noneofthese$

Answer 1

The correct option is B $30thand31st$

Let the two consecutive terms be ${(r-1)}^{th}$ term and $r^h$ term

Co-efficient of ${(r-1)}^{th}$ term and $r^h$ term gives

$=\frac{1}{76-r}\ast \frac{3}{2}=\frac{1}{r-1}$

$3r-3=152-2r$

$5r=155$

$r=31$

So the consecutive terms are ${30}^{th}$ and ${31}^{st}$