Question

Find an explicit form f(n) for each of the following arithmetic sequences (assume a is some real number and x is

some real number).
c. x + 4, x + 8, x + 12, x + 16, ...

Answer 1

Explicit form, f(n) = x +4n

Explanation:

Here the sequence is given as x + 4, x + 8, x + 12, x + 16, ...

First term, f = x + 4

Common difference, d = x + 8 - (x+4) = 4

We have equation for nth term of arithmetic sequence as

`f(n)=a+(n-1)d\\\\f(n)=x+4+(n-1)4=x+4+4n-4=x+4n\\\\f(n)=x+4n`

Explicit form, f(n) = x +4n