Question

How do you find the next three terms of the sequence 2,10,50,250,1250,...?

Answer 1

See below

Explanation:

We are dealing with a geometric squence of ratio 5.

`10/2=5`; `50/10=5`; `250/50=5` etc...

We know general term is given by `a_n=a_1r^(n-1)` with `a_1=2` and `r=5`

In our case `a_n=2·5^(n-1)`

Now for

`n=6` `a_6=2·5^5=6250`
`n=7` `a_7=2·5^6=31250`
`n=8` `a_8=2·5^7=156250`