What is the sixteenth term of the arithmetic sequence: -13√3, -11√3, -9√3, ...?

To determine the sixteenth term of the arithmetic sequence, we first need to identify the common difference between consecutive terms.

The first term of the sequence is -13√3 and the second term is -11√3. The common difference can be calculated by subtracting the first term from the second term:

-11√3 - (-13√3) = -11√3 + 13√3 = 2√3.

Now that we know the common difference (2√3), we can use the formula for the nth term of an arithmetic sequence, which is given by:

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

where:

• ( a_n ) is the nth term,

• ( a_1 ) is the first term,

• ( d ) is the common difference,

• ( n ) is the term number.

For the sixteenth term (n = 16):

[ a_{16} = -13√3 + (16 - 1) * 2√3. ]

This simplifies to:

[ a_{16} = -13√3 + 15 * 2√3, ]

[ a_{16} = -13