Question

The ${15}^{th}$ terms of the series $2\frac{1}{2}+1\frac{7}{13}+1\frac{1}{9}+\frac{20}{23}+$_____ is

• A. $\frac{5}{12}$
• B. $\frac{10}{21}$
• C. $\frac{10}{39}$
• D. None of these

Answer 1

The correct option is C $\frac{10}{39}$

• On solving these improper fractions into proper fraction and by making numerators be 20.
  

we get series as ,

=> $\frac{20}{8}$+$\frac{20}{13}$+$\frac{20}{18}$+$\frac{20}{23}$+$\frac{20}{28}$+............

Therefore , here denominators are in AP having common difference be $5$.

So , $15th$ term of denominator be = $8+14\times 5=78$

Hence $15th$ term of series will be,

=> $\frac{20}{78}$ = $\frac{10}{39}$