Question

Write an equation to describe the sequence below. Use n to represent the position of a term in the sequence, where n=1 for the first term. 84, 168, 252, 336, ... an

Answer 1

`a_(n)` = 1 + (n-1)84

Explanation:

to solve a sequence there's a formula-

`a_(1)`+(n-1)d

where a1 is the first term, and d is the common difference

since we know the first term, and we have a few subsequent terms we can solve for d and creat the general formula for the nth term

to find d we simply check the difference between two terms-

168-x = 84

168-84 = x

84 = x

we can confirm this by checking the next two even

252- x = 168

252 - 168 = x

84 = x

now we have enough for a general formula

`a_(n)` = 1 + (n-1)84