Question

okay so im taking this online math class and i dont know how to do these so can someone help me please.......

Which of the following sequences is not arithmetic?

1, 2, 3, 4, ...
2, 4, 6, 8, ...
0, -2, -4, -6, ...
1, 4, 9, 16, ...

A sequence has a second term of 1 and a common difference of -3.

The fifth term of the sequence is _____.

-11
-8
-5
10

Answer 1

1)
A sequence is arithmetic if the difference between consecutive terms is constant.

$1,2,3,4,... \\ 2-1=3-2=4-3=1 \\ \hbox{arithmetic} \\ \\ 2,4,6,8,... \\ 4-2=6-4=8-6=2 \\ \hbox{arithmetic} \\ \\ 0,-2,-4,-6,... \\ -2-0=-4-(-2)=-6-(-4)=-2 \\ \hbox{arithmetic} \\ \\ 1,4,9,16,... \\ 4-1=3 \not= 9-4=5 \not= 16-9=7 \\ \hbox{not arithmetic}$

1, 4, 9, 16, ... is not an arithmetic sequence.

2)
$a_2=1 \\ d=-3 \\ \\ a_5=a_2+3d \\ a_5=1+3 \times (-3) \\ a_5=1-9 \\ a_5=-8$

The fifth term is -8.