GATE CS 2014 Set 3 QGA-4 — General Aptitude

We can analyze the given series: $2, 5, 10, 17, 26, 37, 50, 64$ by looking at the pattern of the terms.

Method 1: Square of numbers plus 1 ($n^2 + 1$)

• $1^2 + 1 = 2$
• $2^2 + 1 = 5$
• $3^2 + 1 = 10$
• $4^2 + 1 = 17$
• $5^2 + 1 = 26$
• $6^2 + 1 = 37$
• $7^2 + 1 = 50$
• $8^2 + 1 = 65$

The last term in the series is given as $64$ instead of $65$.

Method 2: Difference between consecutive terms

• $5 - 2 = 3$
• $10 - 5 = 5$
• $17 - 10 = 7$
• $26 - 17 = 9$
• $37 - 26 = 11$
• $50 - 37 = 13$
• $64 - 50 = 14$ (should be $15$)

The differences are consecutive odd numbers: $3, 5, 7, 9, 11, 13, 15$. Thus, the last term should be $50 + 15 = 65$.

Therefore, 64 does not belong to the series.