Question

Identify the pattern in the number series and complete the sequence: 2, 5, 10, 17, __, __

• A. 26, 37
• B. 25, 36
• C. 28, 41
• D. 24, 33

Hint:

If the terms aren’t in a simple table, check the first differences—very often they form an easy progression (like consecutive odd numbers).

Answer 1

The Correct Option is A

Solution:
Step 1 (Look at successive differences).
\(5-2=3\), \(10-5=5\), \(17-10=7\).
Step 2 (Spot the pattern).
Differences are consecutive odd numbers: \(3,5,7,\ldots\). Next odd numbers are \(9,11\).
Step 3 (Generate the next terms).
\(17+9=26\).
\(26+11=37\).
Step 4 (Write the completed sequence).
\(2, 5, 10, 17, 26, 37\).
\[ {26,\,37\ \text{(Option (a)}} \]