Question

Find the 14th term of the geometric sequence 5, -10, 20, ...5,−10,20,

Answer 1

-40,960

Explanation:

you have to add the negative because there partners in crime

Answer 2

40,960

Explanation:

To find the multiplier, set up an equation like this:

`5x=-10`

The above equation will allow us to find what number, when multiplied with 5 will result in -10. If we divide both sides of the equation by 5, we'll find that the number, x, is -2:

`x=-2`

We need to find the 14th term. To do this, simply multiply the lattermost number in the sequence by our multiplier, -2.

`20*(-2)=40`

Since 5 is the first term in the sequence, -10 is the second term in the sequence, and 20 is the third term in the sequence, 40 is the fourth term. Now we just need to find the next ten so that we can find the 14th term. To do that, repeat the process of multiplying the lattermost number by -2 ten more times:

`40*-2=-80\\-80*-2=160\\160*-2=-320\\-320*-2=640\\640*-2=-1280\\-1280*-2=2560\\2560*-2=-5120\\-5120*-2=10240\\10240*-2=-20480\\-20480*-2=40960`

Therefore, the 14th term is 40,960.