Question

Find the missing term in the given sequence:

\[ 1,\ 5,\ 5,\ 10,\ 4,\ 15,\ 13,\ \_ \_ \] 

• A. \(17\)
• B. \(16\)
• C. \(9\)
• D. \(20\)

Hint:

Whenever a number series looks irregular, first separate: \[ \text{Odd-position terms} \] and \[ \text{Even-position terms} \] Many reasoning questions contain two independent patterns.

Answer 1

The Correct Option is D

Concept: In number series problems, it is often useful to separate the sequence into odd-position terms and even-position terms. Many competitive examination questions follow two independent patterns simultaneously.

Step 1: Separate odd and even positioned terms.
Given sequence: \[ 1,\ 5,\ 5,\ 10,\ 4,\ 15,\ 13,\ ? \] Odd-position terms: \[ 1,\ 5,\ 4,\ 13 \] Even-position terms: \[ 5,\ 10,\ 15,\ ? \]

Step 2: Observe the pattern in even-position terms.
\[ 5,\ 10,\ 15 \] The difference is: \[ 10-5=5 \] \[ 15-10=5 \] Thus the sequence increases by \(5\) each time. Therefore, \[ 15+5=20 \]

Step 3: Verify consistency.
The even-position sequence becomes: \[ 5,\ 10,\ 15,\ 20 \] which follows a perfect arithmetic progression with common difference \(5\).

Step 4: Determine the missing term.
\[ \boxed{20} \] Hence, option (D) is correct.