Question

Write the explicit formula for the arithmetic sequence.

Answer 1

Option C

The explicit formula for the arithmetic sequence is $a_n = 9 - 6n$

Solution:

Given that the arithmetic sequence is:

3, -3, -9, -15, -21, ...

To find: Explicit formula for the arithmetic sequence

The nth term of an arithmetic sequence is given by:

$a_n = a_1 + (n - 1)d$

Where $a_n$ is nth term of sequence

n is the term's location

$a_1$ is the first term of sequence

d is the common difference between terms

In an arithmetic sequence, the difference between successive terms is constant. This means that we can move from any term to the next one by adding a constant value.

In the given sequence:

3, -3, -9, -15, -21, ...

$a_1 = \text{ first term } = 3$

d = difference between any two terms in sequence

$d = a_2 - a_1$

d = -3 - (3) = -6

Substituting the values in above formula,

$a_n = 3 + (n - 1)(-6)\\\\a_n = 3 -6n + 6\\\\a_n = 9 - 6n$

Thus the explicit formula to find any term in sequence is found