The second term of a Gp is 4 the fifth term is 81 .find the seventh term
A5/A2 = ar^4 / ar = r^3 = 81/4
Now solve for a and r, and then find A7 = ar^6
I suspect a typo.
The second term of a Gp is 4 ---> ar = 4
the fifth term is 81 ---> ar^4 = 81
divide them:
r^3 = 81/4 or 162/8
r = 162^(1/3) / 2
seventh term = ar^6 = ar^4 ( r^2)
= 81(162^(2/3)/4
Are you sure you don't have a typo?
e.g. If instead of r^3 = 81/4 , we would have had r^2= 81/4
this would have worked out so much nicer
There's not a typo please
To find the seventh term of a geometric progression (GP), we need to determine the common ratio and then use the formula for the nth term of a GP.
Given information:
The second term of the GP is 4.
The fifth term of the GP is 81.
Step 1: Find the common ratio (r)
We know that the second term (a₂) is related to the first term (a₁) by the formula a₂ = a₁ * r. Let's substitute the given values into this equation:
4 = a₁ * r.
Step 2: Find the value of a₁.
To find a₁, we can rewrite the equation for the second term (a₂) in terms of a₁:
a₂ = a₁ * r.
We are given that the first term (a₁) does not have a value. Since we don't have enough information to determine a specific value for a₁, we'll leave it as a general variable.
Step 3: Find the value of the common ratio (r)
Substitute the values we know into the equation for the fifth term (a₅):
81 = a₁ * r⁴.
Step 4: Solve for r
To find the value of r, solve the equation from the previous step for r:
r⁴ = 81/a₁.
Step 5: Find the seventh term (a₇)
Using the formula for the nth term of a GP, we can now find the seventh term (a₇).
a₇ = a₁ * r⁶.
Since we don't have a specific value for a₁, we cannot find the exact value of the seventh term (a₇) without additional information. However, if you provide the value of the first term (a₁), I can calculate the seventh term for you.