Question

The $9$th term of the series $27+9+5\frac{2}{5}+3\frac{6}{7}+...$ will be:

• A. $1\frac{10}{17}$
• B. $\frac{10}{17}$
• C. $\frac{16}{27}$
• D. $\frac{17}{27}$

Answer 1

The correct option is A

$1\frac{10}{17}$

Step 1: Finding the general term of the sequence.

The given series is: $27+9+5\frac{2}{5}+3\frac{6}{7}+...$

Writing the general term of the series:

$$\begin{gathered} 27+9+5\frac{2}{5}+3\frac{6}{7}+... \\ =\frac{27}{1}+\frac{27}{3}+\frac{27}{5}+....+\frac{27}{(2n-1)} \\ \therefore T_n=\frac{27}{(2n-1)} \end{gathered}$$

Step 2: Finding the $9$th term.

Substituting $n=9$ in the above equation

$$\begin{gathered} T_n=\frac{27}{(2n-1)} \\ {T}_n=\frac{27}{18-1} \\ {T}_n=\frac{27}{17}=1\frac{10}{17} \end{gathered}$$

Hence, the value of $T_9=1\frac{10}{17}$

Therefore, the correct answer is Option (A).