Question

The tenth, eleventh, and twelfth terms of a sequence are shown in the table below:


Term number 10 11 12
Term -34 -38 -42


Which of the following shows the first five terms of the sequence?
A. -2, 2, 6, 10, 14

B. 2, -2, -6, -10, -14

C. -2, -6, -10, -14, -18

D. 2, 6, 10, 14, 18

Answer 1

this just looks to be a sequence where each number is added by 4

Answer 2

you can use the process of elimination by seeing which sequence follows the same pattern.

Answer 3

I don't inderstand the sequence

Answer 4

And I'm sorry I should have said the sequence is subtracted by 4

Answer 5

\[-34-4 = -38, -38-4= -42\]

Answer 6

so you take a look at the answers you are given and see which series follows the same pattern where the numbers become more negative as 4 is subtacted from the previous number within the series

Answer 7

there are two you can be sure of that are wrong immediately by recognizing this pattern

Answer 8

let the first number be a and common difference be d [ i said common difference because there's a common difference between the numbers of sequence ]
so the 1st term will become a
2nd term will become a+d = d + a = d + first term
3rd term will become a+2d = a +d +d = d+ 2nd term
4th term will become a+3d = a+ d +2d = d+3rd term
get it till this point?

Answer 9

Would the closest be C?

Answer 10

C is correct yes

Answer 11

well done

Answer 12

yay!!

Answer 13

do you understand why or was that a guess?

Answer 14

if you look when you add -4 to -2 you get -6

Answer 15

no i understand. I was also asking to see if i was right.

Answer 16

ok, then good job

Answer 17

thanks.

Answer 18

B seems more correct:

common difference = -4
so if the first term was 'a', then the tenth term will be
\[a - 4*(10 - 1) = -34\]
solve this equation for a to get
\[a = 2\]
so the sequence should start with 2, which means that it can be either B or D

Now B is decreasing by 4 whereas D is increasing by 4. Since the given sequence decreases by 4, hence B is correct

Answer 19

I just looked on the internet. Another person said it's B ok thanks for the help.

Answer 20

its arithmetic sequence, so to get the nth term you have formula
nth term = a +(n-1)*d
so here 10 th term he gave it as -34
10th term = a + (10-1)*d = a + 9d = -34
\[a + 9*d = -34 ---( 1)\]
then 11th term = a + (11 -1)*d = a + 10d = -38
\[a + 10*d = -38 ---(2)\]
we know before hand that d is -4, so in (1) if we substitute d value we get a
a = -34 -9*(-4)
a = -34 + 36 = 2
so first term is 2 , now just -4 ( or subtract 4) to it to get next item and vice versa