Which expression gives the number in the nth position in the sequence: 2, 5, 8, 11?
a) 2n + 2 b) 2n c) 3n - 1 d) 3n + 3 e) 4n

Solution:

An arithmetic progression is a sequence of numbers that have a common difference between two consecutive terms. Geometric Progression is a sequence of numbers that are related by a common ratio. These progressions find their applications in various fields of mathematics and science.

The given sequence: 2, 5, 8, 11

⇒ Common difference = 5 - 2 = 3

⇒ n^th term is given by a_n = a₁ + (n - 1)d, where a₁ is the first term and d is the common difference.

⇒ Using the above formula, we get a_n = 2 + (n - 1)3 = 3n - 1

Hence, the nth position of the sequence 2, 5, 8, 11 is given by 3n - 1.

Which expression gives the number in the nth position in the sequence: 2, 5, 8, 11?

Summary:

The nth position of the sequence 2, 5, 8, 11 is given by 3n - 1.