Question

1) Use the sequence below to complete each task. -23, -18, -13, -8, ... a. Identify the common difference (a). b. Write an equation to represent the sequence. C. Find the 13th term (23) Ginawson The Alptra). 2013

Answer 1

(a) The common ratio is 5

(b) The equation that represents the sequence is:

`T_n=5n-28`

(c) The 13th term is 37

Step-by-step explanation:

Given the sequence:

-23, -18, -13, -8, ...

(a)

The Common difference is obtained by subtracting a term from it succeeding term.

-18 - (-23)

= -18 + 23

= 5

OR

-13 - (-18)

= -13 + 18

= 5

OR

-8 - (-13)

= -8 + 13

= 5

(b)

To write the equation that represents the sequence, we make use of the formula:

`\begin{gathered} T_n=a+(n-1)d \\ \\ \text{Where a is the first term, and d is the common difference} \end{gathered}`

a = -23, d = 5

Using these, we have:

`\begin{gathered} T_n=-23+(n-1)*5 \\ =-23+5n-5 \\ =5n-28 \end{gathered}`

(c) To find the 13th term, we use the formula above

`\begin{gathered} T_(13)=5(13)-28 \\ =65-28 \\ =37 \end{gathered}`