Question

Which of the following is a Recursive Formula for an Arithmetic Sequence?

a1 = -2, an = an-1 + 5
an = 5n – 7
a1 = -2, an= 5an-1
an = -2 + 5(n – 1)

Answer 1

The correct answer is Option 1: a1 = -2, an = an-1 + 5

Explanation:

A recursive formula is a formula that uses previous term in order to calculate the next term in a sequence.

In case of arithmetic sequence, the next term is obtain by adding a specific number to the last term.

This can be written as:

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

Here

a_n is the terms we are calculating

a_{n-1} is the previous term and d is the common difference.

If we compare the given options, we can see that only option 1 matches with the general form of recursive formula

an = an-1 + 5

Here

5 is the common difference

Hence,

The correct answer is Option 1: a1 = -2, an = an-1 + 5