In one arithmetic sequence we have : next term = previous term + number

In your example we will have...

t1+x=t2

t2=9

t3=t2+x

t4=t3+x

t5=t4+x

t5=21

By doing the replacements we get :

21=t4+x 21=t3+x+x 21=t2+x+x+x 21=9+3x 3x=12 x=4

So we have t1=5 , t2=9 , t3=13 , t4=17 , t5=21 , t6=25 .... and we can find that t10=41

In geometric sequence we have : next term=previous term*number (say y). Here we have :

t2=8

t3=8*y

t4=t3*y

Working like before we find y=3 or y=-3

Now you can find t6.

Hope this is what you want...