Question

Which of the following are arithmetic sequences? a. -2,2,6,10 b. 1,3,9,27 c. 5,10,20,40 d. 5,1,-3,-7

Answer 1

how do we define a sequence as arithmetic?

Answer 2

In arithmatic sequences, the difference is found by addition.
In geometric sequences, the differences are found by multiplication

Answer 3

If a sequence of values follows a pattern of adding a fixed amount from one term to the next, it is referred to as an arithmetic sequence

Answer 4

Please help

Answer 5

take the terms and see if you add the same amount to the first one to get the to second one, as you do to get from the second to third

Answer 6

\[t_2-t_1=n\]
\[t_3-t_2=k\]
if n=k, your good to go in general

Answer 7

look at your answer choices
you have to find the pattern.
can you add anything to the first term to get to the second term ?
can you add the same number to the second term to get to the third term ?

Answer 8

of course order is immaterial as long as you get the same value .....

for example:

-2,2,6,10

-2 - 2 = -4
2 - 6 = -4
6 - 10 = -4

that is one of them ... i believe there is one more

Answer 9

1,3,9,27

1 - 3 = -2
3 - 9 = -6 so this isnt the same each time ...

try the others to test them out

Answer 10

Here is an example of an arithmetic sequence...
3,5,7,9,11
3 + 2 = 5
5 + 2 = 7
7 + 2 = 9
your common difference is 2 (by addition)

geometric sequence example
3,6,12,24
3 x 2 = 6
6 x 2 = 12
12 x 2 = 24
your common difference is 2 (by multiplication)

Answer 11

i might sound really stupid but how exactly do you do this

Answer 12

ok so you added two to get from 3 to 5 and 5 to seven so its added by two ok i get that

Answer 13

look at your first answer choice...
-2,2,6,10
take your second term and subtract your first term
-2 - (-2) = 4
now take your third term and subtract your second term
6 - 2 = 4
4th term subtract 3rd term
10 - 6 = 4
common difference is 4, and you can add 4 to each term to get the next number.
This is an arithmetic sequence.

Answer 14

okay i get it know thankyou

Answer 15

now

Answer 16

glad to help :)