Question

What will be the next term in the sequence?
\( \frac{17}{14}, \frac{18}{13}, \frac{16}{15}, \frac{19}{12}, \frac{?}{?} \)

• A. \( \frac{20}{13} \)
• B. \( \frac{21}{25} \)
• C. \( \frac{15}{16} \)
• D. \( \frac{17}{18} \)

Hint:

For fraction series, also check if there is an alternative pattern of jumping terms:
- Numerators: \( 17 \rightarrow 16 \) (\( -1 \)), \( 18 \rightarrow 19 \) (\( +1 \)).
- Denominators: \( 14 \rightarrow 15 \) (\( +1 \)), \( 13 \rightarrow 12 \) (\( -1 \)).
This alternate-term method often yields the same correct answer faster and with less computation!

Answer 1

The Correct Option is C

Step 1: Separate numerators and denominators.
Numerators: $17,18,16,19$; denominators: $14,13,15,12$. Treat them as two series.
Step 2: Find the numerator pattern.
Differences are $+1,-2,+3$, alternating with growing size, so next is $-4$.
Step 3: Get the next numerator.
$19-4=15$.
Step 4: Find the denominator pattern.
Differences are $-1,+2,-3$, so next is $+4$.
Step 5: Get the next denominator.
$12+4=16$.
Step 6: Combine into the next term.
The fraction is $\dfrac{15}{16}$.
\[ \boxed{\dfrac{15}{16}} \]