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

Answer:

$a_1=-10$

$d=3$

Step-by-step 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 $d=3$