Question

Which pattern does this sequence follow: 1, 5, 12, 22, 35, 51, 70…?

• A. Square number pattern
• B. Pentagonal number pattern
• C. Hexagonal number pattern
• D. Triangle number pattern

Answer 1

The correct option is B Pentagonal number pattern

1, 5, 12, 22, 35, 51, 70…

The pentagonal number sequence is a pattern of numbers which follows the following rule.

The number in nth position =[$3^{\ast }{n}^{\ast }(n-1)/2$] + n

For example:

The number in 4th position = [$3^{\ast }{4}^{\ast }3/2$] + 4 = (36/2) + 4 =18 + 4 = 22

The number in 6th position= [$3^{\ast }{6}^{\ast }5/2$] + 6 = (90/2) + 6 = 45 + 6 = 51