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
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.
Answer: The nth position of the sequence 2, 5, 8, 11 is given by 3n - 1.
Let's understand the solution.
The given sequence: 2, 5, 8, 11
⇒ Common difference = 5 - 2 = 3
⇒ nth term is given by an = a1 + (n - 1)d, where a1 is the first term and d is the common difference.
⇒ Using the above formula, we get an = 2 + (n - 1)3 = 3n - 1