Question

write an explicit formula for the sequence
4, 1.5, -1, -3.5

Answer 1

what have you tried?

Answer 2

well i figured out how to write the recursive formula but I cant figure out the explicit

Answer 3

show me the recurrsive

Answer 4

\[A _{n}=A _{n-1}-2.5\]

Answer 5

your missing a part, a recurrsive rule as the equation part, and also an A1 part. You need to be able to define where the sequence starts at.

Answer 6

where A1 = 4

Answer 7

good

A1 = 4
A2 = A1 - 2.5
A3 = A2 - 2.5
A4 = A3 - 2.5

you agree that this is how it would progress recurrsively then right?

Answer 8

if so, then lets start defining the An terms in just A1

A1 = 4

A2 = A1 - 2.5 = 4 - 2.5

A3 = A2 - 2.5 = 4 - 2.5 - 2.5 = 4 -2.5(2)

A4 = A3 - 2.5 = 4 - 2.5 - 2.5 - 2.5 = 4 -2.5(3)

.....................

or to clean it up some lets write them like this

A1 = 4 - 2.5(0)

A2 = 4 - 2.5(1)

A3 = 4 -2.5(2)

A4 = 4 -2.5(3)


notice that the nth A follows a pattern: An = 4 - 2.5(n-1) seems to fit

Answer 9

okay im kindof confused