the 3rd term of a gpis 10 and the 6th term is 80 find the common ratio No2 if the 2nd term of a gp is 4 and the 5th term is 1over 16,the7th term is_

a , ar , ar^2 , ar^3 , ar^(n-1)

ar^2 = 10
ar^5 = 80

ar^5 / ar^2 = 8

r^3 = 8

r = 2
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now you do the second one.

a smart student

If first term of a g.p 3 and 4 what is third term

A. P.s.Its 5th and 10th

term are
86 and 146 respectively

Adam

nothing but i will try to learn it well though i am a smart student

To find the common ratio of a geometric progression (GP), we can use the formula:

nth term = a * r^(n-1),

where "a" is the first term, "r" is the common ratio, and "n" is the term number.

Let's solve the first problem:
Given that the 3rd term of the GP is 10 and the 6th term is 80, we can write two equations:

10 = a * r^(3-1) Equation 1
80 = a * r^(6-1) Equation 2

We can rewrite Equation 1 to get the value of "a":
10 = a * r^2

Next, we divide Equation 2 by Equation 1 to eliminate "a":
80 / 10 = (a * r^(6-1)) / (a * r^2)
8 = r^5

Taking the fifth root of both sides to solve for "r":
∛∛∛∛8 = ∛r^5
2 = r

Therefore, the common ratio of the geometric progression is 2.

Now let's solve the second problem:
Given that the 2nd term of the GP is 4 and the 5th term is 1/16, we can write two equations:

4 = a * r^(2-1) Equation 1
1/16 = a * r^(5-1) Equation 2

Again, we can rewrite Equation 1 to solve for "a":
4 = a * r

Divide Equation 2 by Equation 1:
(1/16) / 4 = (a * r^(5-1)) / (a * r)
(1/64) = r^4

Taking the fourth root of both sides to solve for "r":
∜∜∜∜(1/64) = ∜r^4
(1/4) = r

Therefore, the common ratio of the second geometric progression is 1/4.