Question

The first several terms of a sequence {an} are: 6,10,14,18,22,.... Assume that the pattern continues as indicated, find an explicit formula for an.

Answer 1

The explicit formula for an is :

an = a1 + (n - 1)d

Where n = nth term

d = common difference

a1 = First term

Therefore:

an = 6 + (n -1)4

Explanation:

We have sequence: 6,10,14,18,22

The first term = a or a1 = 6

The difference between these terms = second term - first term = Third term - second term

10 - 6 = 14 - 10

= 4

Hence,

The explicit formula for an is :

an = a1 + (n - 1)d

Where n = nth term

d = common difference

a1 = First term

Therefore:

an = 6 + (n -1)4