Question

Write an explicit equation for the arithmetic sequence
3,7,11,15,19​

Answer 1

`a_(n)` = 4n - 1

Explanation:

The n th term ( explicit equation) of an arithmetic sequence is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 3 and

d = 7 - 3 = 11- 7 = 4

Hence

`a_(n)` = 3 + 4(n - 1) = 3 + 4n - 4 = 4n - 1

Answer 2

t_x = 3 + 4x

Where t_x is term x, and x = 0, 1, 2, ...

If you want x to begin at 1 then use the equation
t_x = 3 + 4(x - 1)