Question

Find the missing term in the series: \[ (2,0);\;(5,3);\;(10,8);\;(\_\_\_);\;(26,24);\;(37,35);\;(50,48);\;(65,63);\;(82,80) \]

• A. \((13,11)\)
• B. \((14,12)\)
• C. \((20,18)\)
• D. \((17,15)\)

Hint:

For ordered pair series, analyze each component separately. Most of the time both follow the same numerical pattern.

Answer 1

The Correct Option is D

Concept: Observe both numbers in each pair separately. Usually in paired series, both coordinates follow related patterns.

Step 1: Observe the first numbers.
\[ 2,\;5,\;10,\;\_,\;26,\;37,\;50,\;65,\;82 \] Differences: \[ +3,\;+5,\;+7,\;+9,\;+11,\;+13,\;+15,\;+17 \] So missing first number: \[ 10+7=17 \]

Step 2: Observe the second numbers.
\[ 0,\;3,\;8,\;\_,\;24,\;35,\;48,\;63,\;80 \] Differences: \[ +3,\;+5,\;+7,\;+9,\;+11,\;+13,\;+15,\;+17 \] So missing second number: \[ 8+7=15 \]

Step 3: Form the missing pair.
Thus: \[ (17,15) \] Hence, the required answer is: \[ \boxed{(17,15)} \]