Question

3 Use the sequence below to complete each task. -13, -15, -17, -19, ... a. Identify the common difference (d). b. Write an equation to represent the sequence. C. Find the 15th term (as) WIE A Alta

Answer 1

The given sequence is

`-13,-15,-17,-19,\ldots`

As you can notice, this sequence is about negative numbers only, also, the number is increasing in the absolute value of 2 units each time. This means its difference is -2, let's prove it

`\begin{gathered} -13-2=-15 \\ -15-2=-17 \\ -17-2=-19 \end{gathered}`

So, the answer to (a) is 2.

This arithmetic sequence can be defined with the following formula

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

Where,

`\begin{gathered} a_1=-13 \\ d=-2 \end{gathered}`

Replacing these values, we find the equation for the sequence

`\begin{gathered} a_n=-13+(n-1)(-2) \\ a_n=-13-2n+2 \\ a_n=-2n-11 \end{gathered}`

Therefore, the answer so (b) is

`a_n=-2n-11`

At last, to find the 15th term, we just replace n=15 in the equation

`a_(15)=-2(15)-11=-30-11=-41`

Therefore, the answer to (c) is -41.