Question

Q29
Please help me as soon as possible.

Answer 1

`\textsf{D.} \quad (12)/(13)`

Explanation:

The given number pattern is:

`(2)/(3),\;(3)/(4),\;(5)/(6),\;(8)/(9),\;...`

The first fraction is 2/3.

The second fraction is 3/4, which can be written as (2 + 1) / (3 + 1).

The third fraction is 5/6, which can be written as (3 + 2) / (4 + 2).

The fourth fraction is 8/9, which can be written as (5 + 3) / (6 + 3).

From the observed pattern, it appears that:

• Each numerator is the sum of the previous numerator and the position of the previous term.
• Each denominator is the sum of the previous denominator and the position of the previous term.

Therefore, to find the next term, we can apply this pattern:

`\begin{aligned}\sf Numerator &=\sf previous\; numerator+position \;of \;the\; previous\; term\\&=\sf 8+4\\&=\sf 12\end{aligned}`

`\begin{aligned}\sf Denominator&=\sf previous\; denominator+position \;of \;the\; previous\; term\\&=\sf 9+4\\&=\sf 13\end{aligned}`

Therefore, the next term in the pattern is:

`\Large\boxed{\boxed{(12)/(13)}}`