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).
a. −34, −22, −10, 2, ...

Answer 1

f(n) =
`a_(n)= -34 + 12(n-1)`

Explanation:

The explicit form of an arithmetic sequence is given by the formula:

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

an= nth term

a1= first term

d= common difference

In this case, a1= -34

In order to obtain the value of the common difference you have to subtract two consecutive terms of the sequence (The largest minus the smallest)

-22 - (-34) = 12

To confirm that it's the common difference, subtract another two consecutive terms:

-10 - (-22) = 12

Therefore d=12

Replacing in the formula:

`a_(n)= -34 + 12(n-1)`