# In an arithmetic sequence, a17 = -40 and a28 = -73. Write a recursive formula for this sequence.

## Question:

In an arithmetic sequence, a17 = -40 and a28 = -73. Write a recursive formula for this sequence.

## Arithmetic Sequence and Recursive Formula:

An arithmetic sequence is a sequence of numbers (positive or negative) containing a property that every next term is found by adding a constant term to the previous and this value of addition is known as the common difference and designated as {eq}d. {/eq}

If {eq}a {/eq} is the first term and {eq}d {/eq} is the common difference of an arithmetic sequence then the representation of an arithmetic sequence is given as-

$$a,a+d,a+2d,,.................$$

The general term formula is a formula that is used for the calculation of any term of the sequence by using the values of the first term and the common difference.

The general term formula of an arithmetic sequence is written as-

$$a_{n} = a+(n-1)d$$

where {eq}a_{n} {/eq} is the nth term

The recursive formula is a formula that is derived by putting the values of the first term and the common difference in the arithmetic sequence.

\begin{align} a_{17} &= -40 \\[0.2cm] a+(17-1)d &= -40 \\[0.2cm] a+16d &= -40 \tag{Eq.1}...