Question

Find the second, fourth, and eleventh terms of the

sequence described by each explicit formula.

A(n) = -9 + (n - 1)(3)
​

Answer 1

Second term = -6

Fourth term = 0

Eleventh term = 21

Explanation:

We are given the following explicit formula of an arithmetic sequence and we are to find the second, fourth and the eleventh terms of this sequence:

`a_n=-9+(n-1)(3)`

where
`a_n` = nth term,
`a_1=-9` and
`n` = number of term.

Second term
`(a_2) = -9+(2-1)(3)` = -6

Fourth term
`(a_4) = -9+(4-1)(3)` = 0

Eleventh term
`(a_(11)) = -9+(11-1)(3)` = 21

Answer 2

The second term is -6 , the fourth term is 0 , the eleventh term is 21

Explanation:

* Lets revise the explicit formula

- An explicit formula will create a sequence using n, the number

position of each term.

- If you can find an explicit formula for a sequence, you will be able

to quickly and easily find any term in the sequence by replacing

n with the number of the term you want

- It defines the sequence as a formula in terms of n.

* Now lets solve the problem

- The formula of the sequence is A(n) = -9 + (n - 1)(3)

- A(n) is any term in the sequence

- n is the position of the number

- To find the second term put n = 2

∵ n = 2

∴ A(2) = -9 + (2 - 1)(3) = -9 + (1)(3) = -9 + 3 = -6

* The second term is -6

- To find the fourth term put n = 4

∵ n = 4

∴ A(4) = -9 + (4 - 1)(3) = -9 + (3)(3) = -9 + 9 = 0

* The fourth term is 0

- To find the eleventh term put n = 11

∵ n = 11

∴ A(11) = -9 + (11 - 1)(3) = -9 + (10)(3) = -9 + 30 = 21

* The eleventh term is 21