Question

Find 8th term for 10,-20,40

Answer 1

-1280

Explanation:

So, as we can see just by loooing at this geometric sequence, the factor is -2. Let's double check this.

10 * -2 = -20 * -2 = 40

We can just keep multiplying to find the 8th term!

40 * -2 = -80 * -2 = 160 *-2 = -320 * -2 = 640 * -2 = -1280

Sometimes with a short sequence, it is better to just multiply it out. You could also do it like this, though:

`a_(n)=a_(1) *r^(n-1)`

Here, r = -2. We are looking for the 8th term, which would be 8

Plug in our values:

`a_(8)=10*-2^(7)`

`-2^(7)=-128\\`

`10*-128=-1280`

That is the same answer we got before. I would suggest doing it mathematically if you have a long sequence (15, 100, 300 terms)

Hope this helped!