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: Understanding the Question:
We need to determine the next term in the given fractional sequence by finding separate mathematical patterns for the numerators and the denominators.

Step 2: Detailed Explanation:
Let us analyze the numerators and denominators as two independent series:
1. Numerator Series:
The numerators are: \( 17, 18, 16, 19 \)
Let us observe the differences:
- \( 17 \rightarrow 18 \) (differs by \( +1 \))
- \( 18 \rightarrow 16 \) (differs by \( -2 \))
- \( 16 \rightarrow 19 \) (differs by \( +3 \))
The pattern of differences is an alternating sequence of addition and subtraction with increasing integers: \( +1, -2, +3, -4, \dots \)
Therefore, the next numerator must be:
- \( 19 - 4 = 15 \)
2. Denominator Series:
The denominators are: \( 14, 13, 15, 12 \)
Let us observe the differences:
- \( 14 \rightarrow 13 \) (differs by \( -1 \))
- \( 13 \rightarrow 15 \) (differs by \( +2 \))
- \( 15 \rightarrow 12 \) (differs by \( -3 \))
The pattern of differences is an alternating sequence of subtraction and addition with increasing integers: \( -1, +2, -3, +4, \dots \)
Therefore, the next denominator must be:
- \( 12 + 4 = 16 \)
Combining the two results, the next term in the sequence is \( \frac{15}{16} \).

Step 3: Final Answer:
(C) \( \frac{15}{16} \)