Write the explicit formula for the arithmetic sequence.

3, -3, -9, -15, -21,
a) an = 7 - 4n
b) an = 6 - 3n
c) an = 9 - 6n
d) an = 18 - 15n

Option C

The explicit formula for the arithmetic sequence is

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:

Where is nth term of sequence

n is the term's location

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, ...

d = difference between any two terms in sequence

d = -3 - (3) = -6

Substituting the values in above formula,

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

answer: a

step-by-step explanation: the answer is a due to the rule of symmetry; that a line of symmetry must divide a figure into 2 pieces that are the exact same, only reflected over a line of symmetry. b and c do not have lines of symmetry and would not divide the figure evenly, thus making the answer a.