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Q: fnd the two consecutive terms in the expansion of (3+2x)⁷⁴so that the coeffs of powers of x are equal.

$Let the two consecutive terms be (r - 1)^{th} {t erm and r}^{t h} term \Rightarrow Coefficient of (r - 1)^{th} and r^{t h} t e r m are {}^{74}{C_{r - 2} 3^{74 - r + 2} 2^{- 2} and} {}^{74}{C_{r - 1} 3^{74 - r + 1} 2^{- 1}} From the give data {}^{74}{C_{r - 2} 3^{76 - r} 2^{- 2} =} {}^{74}{C_{r - 1} 3^{75 - r} 2^{- 1}} \Rightarrow \frac{1}{76 - r} \frac{3}{2} = \frac{1}{r - 1} \Rightarrow 3 r - 3 = 152 - 2 r \Rightarrow 5 r = 155 \Rightarrow r = 31 So t {he consecutive terms are 30}^{t h} {and 31}^{t h} term$

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