Question

What is the common difference for the sequence shown below?

coordinate plane showing the points 1, 4; 4, 3; and 7, 2

Answer 1

@jim_thompson5910

Answer 2

It seems like (1,4), (4,3) and (7,2) represent the idea that

first term = 4
fourth term = 3
seventh term = 2

Answer 3

ya

Answer 4

if that is the case, then imagine 7 slots

Answer 5

let's label them A through G

Answer 6

A is the first term
B is the second
and so on...

Answer 7

ok

Answer 8

first term = 4
fourth term = 3
seventh term = 2

so
A = 4
D = 3
G = 2

Answer 9

let's make x the common difference

x is some unknown number

the next term for slot B will be 4+x. This is because we add on the common difference to the previous term to get the next term

first term = 4
second term = 4+x

A = 4
B = 4+x

Answer 10

making sense so far?

Answer 11

yes

Answer 12

the term for slot C is (4+x)+x = 4+x+x = 4+2x


first term = 4
second term = 4+x
third term = 4+2x

A = 4
B = 4+x
C = 4+2x