Question

Write the following Arithmetic Sequence using an Explicit Formula: a 1 =14,a n =a n-1 -6

an = 6 – 14(n – 1)
an = 6 + 14(n – 1)
an = 14 + 6(n – 1)
an = 14 – 6(n – 1)

Answer 1

a_n = 14 - 6(n-1)

Explanation:

To find the explicit formula for the given arithmetic sequence, we need to first find the common difference.

a_n = a_{n-1} - 6

We can see that the common difference is -6. Now, we can use the formula for an arithmetic sequence:

a_n = a_1 + (n-1)d

where a_1 is the first term, d is the common difference, and n is the term number.

We are given a_1 = 14 and d = -6, so we can substitute these values into the formula:

a_n = 14 + (n-1)(-6)

Simplifying this expression, we get:

a_n = 14 - 6(n-1)

Therefore, the explicit formula for the given arithmetic sequence is a_n = 14 - 6(n-1).