Answer:
5^2,5^4,5^6,5^8,5^10
Explanation:
You are given 2nd term is 5^4 and 5th term is 5^10.
Since this is a geometric sequence, the sequence is of the form:
a,ar,ar^2,ar^3,ar^4,....
So setting up a proportion we can find the common ratio r:
(ar^4)/(ar)=(5^10)/(5^4)
Simplifying both sides:
r^3=5^6
r=5^(6/3)
r=5^2
If ar=5^4 and r=5^2 then a=5^2. Why? Because 5^2×5^2=5^4.
So
a=5^2
ar=5^2(5^2)=5^4
ar^2=5^2(5^2)^2=5^2(5^4)=5^6
ar^3=5^2(5^2)^3=5^2(5^6)=5^8
ar^4=5^2(5^2)^4=5^2(5^8)=5^10
So fill in time into:
a,ar,ar^2,ar^3,ar^4,....
5^2,5^4,5^6,5^8,5^10,....