Question

Use the equation below to answer the question.

y = 3x + 6
Which equivalent equation is correctly matched with a key feature of the graph of the function it represents?

Answer 1

Answer:

The signa notation to represent the first five ten f(x) is given by
`f(x)=\sum\limits^(5)_(n=1)a_n`

Explanation:

Given sequence is -5, -9, 13...

Let f(x) be the given sequence and is denoted by

`f(x)=\{-5,-9,-13,...\}`

Let the first term be
`a_1, 2^{\textrm{nd}}` term be
`a_3,...`

ie,
`a_1=-5,a_2=-9, a_3=-13,...`

To find the common difference d:

`d=a_2-a_1`

`=-9-(-5)`

`=-9-(+5)`

`d=-4`

`d=a_3-a_2`

`=-13-(-9)`

`=-13+9`

`d=-4`

Therefore the common difference d is -4 for given sequence f(x) with
`a_1=-5` and d=-4, the seqence f(x) is an arithmetic sequence

By defintion of arithmetic sequence

`a_n=a+(n-1)d\hfill(1)`

Now to find
`a_4, a_5`:

put n=4 in equation (1)

`a_4=a+(4-1)d`

`a_4=-5+(3)(-4)` [since a=-5, d=-4]

`=-5-12`

`a_4=-17`

in equation (1)

`a_5=a+(5-1)d`

`a_5=-5+(4)(-4)` [since a=-5, d=-4]

`=-5-16`

`a_5=-21`

Therefore
`a_4=-17` and
`a_5=-21`

Therefore
`f(x)=\{-5,-9,-13,-17,-21,...\}`

Now to represent the sum of the first five terms of f(x) using sigma notation as below

`f(x)=\sum_(n=1)^5 a_n`

where
`\sum_(n=1)^5 a_n=a_1+a_2+a_3+a_4+a_5`

`-5-9-13-17-21`

`\sum_(n=1)^5 a_n=-65`