Question

Use the graph below to determine a1 and d for the sequence. graphed sequence showing point 1, negative 10, point 2, negative 7, point 3, negative 4, point 4, negative 1, point 5, 2, and point 6, 5

Answer 1

a1=-10; d=3

Explanation:

Answer 2

`a_1=-10`

`d=3`

Explanation:

we know that

In an Arithmetic Sequence the difference between one term and the next is a constant, and this constant is called the common difference (d)

In this problem we have the ordered pairs

`(1,-10),(2,-7),(3,-4),(4,-1),(5,2),(6,5)`

Let

`a_1=-10\\a_2=-7\\a_3=-4\\a_4=-1\\a_5=2\\a_6=5`

Find the difference between one term and the next

`a_2-a_1=-7-(-10)=3`

`a_3-a_2=-4-(-7)=3`

`a_4-a_3=-1-(-4)=3`

`a_5-a_4=2-(-1)=3`

`a_6-a_5=5-2=3`

The difference between one term and the next is a constant

This constant is the common difference

so

The sequence graphed is an Arithmetic Sequence

therefore

The first term is
`a_1=-10`

The common difference is equal to
`d=3`