Question

A recursive rule for an arithmetic sequence is a1=4;an=an−1−3 . What is the explicit rule for this sequence? Enter your answer in the box. an=

Answer 1

The explicit rule for the arithmetic sequence is given by:

`a_n = a_1+(n-1)d` ......[1]

where,

`a_1` is the first term

n is the number of terms and

d is the common difference for two consecutive terms.

As per the statement:

A recursive rule for an arithmetic sequence is:

`a_1 = 4`

`a_n = a_(n-1)-3`

The recursive formula for the arithmetic sequence is given by:

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

then;

On comparing we get;

d = -3

Substitute the given values in [1] we have;

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

⇒
`a_n = 4 -3n+3 = 7-3n`

Therefore, the explicit rule for this sequence is,
`a_n = 7 -3n`