The common ratio is 3 if the 7th term is greater than the first by 65, find the 7th term
I think I know you do you go to OCA?
a*3^6 = a+65
To find the 7th term, we can use the formula for the nth term of a geometric sequence:
an = a1 * r^(n-1)
Where:
an = nth term
a1 = first term
r = common ratio
n = term number
Given that the common ratio is 3, we have:
an = a1 * 3^(n-1)
We are also given the information that the 7th term is greater than the first term by 65:
a7 = a1 + 65
Now we can solve for the 7th term by substituting the known values into our equations.
First, let's rewrite the equation for the 7th term by substituting the given value for a7:
a7 = a1 + 65
Using the formula for the nth term, we can also write:
a7 = a1 * 3^(7-1)
Now we have two equations for a7. We can equate them:
a1 + 65 = a1 * 3^6
Simplifying further:
65 = a1 * 3^6 - a1
Combining like terms:
65 = a1 * (3^6 - 1)
Now we can solve for a1:
65 / (3^6 - 1) = a1
We can then substitute the value of a1 back into the equation for a7 to find the 7th term:
a7 = a1 * 3^6
And that's how you can find the 7th term given a common ratio of 3 and the 7th term being greater than the first term by 65.