The 50th term in the sequence $5,6 x, 7 x^{2}, 8 x^{3}, 9 x^{4}, \ldots$ is
(A) $54 x^{49}$
(B) $54 x^{50}$
(C) $45 x^{50}$
(D) $55 x^{49}$
(E) $46 x^{51}$
The 50th term in the sequence $5,6 x, 7 x^{2}, 8 x^{3}, 9 x^{4}, \ldots$ is
(A) $54 x^{49}$
(B) $54 x^{50}$
(C) $45 x^{50}$
(D) $55 x^{49}$
(E) $46 x^{51}$

## Solution

If we start by looking at the numerical coefficient of each term we make the observation that if we add 1 to 5 to get the second term and 2 to 5 to get the third term we will then add 49 to 5 to get the fiftieth term. Thus the fiftieth term has a numerical coefficient of 54 .

Similarly, if we observe the literal coefficient of each term, the first term has a literal coefficient of $x^{0}$ which has an exponent of 0 . The second term has an exponent of 1 , the third an exponent of 2 so that the exponent of the fiftieth term is 49 which gives a literal part of $54 x^{49}$.

Thus the fiftieth term is $54 x^{49}$.

ANSWER: (A)