Question

Given the sequence 38, 32, 26, 20, 14, ..., find the explicit formula.

Answer 1

`\huge\boxed{a_n=-6n+44}`

Explanation:

This is an arithmetic sequence:

32 - 38 = -6

26 - 32 = -6

20 - 26 = -6

14 - 20 = -6

The common difference d = -6.

The explicit formula of an arithmetic formula:

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

Substitute:

`a_1=38;\ d=-6`

`a_n=38+(n-1)(-6)` use the distributive property

`a_n=38+(n)(-6)+(-1)(-6)\\\\a_n=38-6n+6\\\\a_n=-6n+(38+6)\\\\a_n=-6n+44`

Answer 2

The explicit formula for the sequence is

44 - 6n

Explanation:

The above sequence is an arithmetic sequence

For an nth term in an arithmetic sequence

A(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

From the question

a = 38

d = 32 - 38 = - 6 or 20 - 26 = - 6 or

14 - 20 = - 6

So the formula for the sequence is

A(n) = 38 + ( n - 1)-6

= 38 - 6n + 6

We have the final answer as

A(n) = 44 - 6n

Hope this helps you