Question

30 points please help me

Which choice is the simple formula for the nth term of the following arithmetic sequence?

6, 2, -2, -6, -10, ...

Answer 1

Hey there,

Your question states: Which choice is the simple formula for the nth term of the following arithmetic sequence?

6, 2, -2, -6, -10, 6, -6, 10

If you see,(6,2) are 4 apart. And also (-2,-4) So this would include that (-10,6) because they are also 4 apart.

Hope this helps.
~Jurgen

Answer 2

Given sequence:
6,2,-2,-6,-10,...
First we have to find the common difference.
d= 2-6=-4
d=-2-2=-4
d=-6-(-2)=-6+2=-4
So common difference is -4.

Which means it is an arithmetic sequence.

Formula for the given sequence is:
an= a1+ (n-1)d
an=6+(n-1)(-4)
an=6-4n+4
an=-4n+10

Answer: an=-4n+10