Fill in the blanks for the geometric sequence
__, 5^4, __, __, 5^10

5^2,5^4,5^6,5^8,5^10

Step-by-step 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,

m a t h w a y. c o m

step-by-step explanation: