Question

The first term of a geometric sequence is 4 and the last term is 324. Find the sum if the ratio of 2 successive terms is 3.

Answer 1

In order to use any of the summation formulas, we need to know the total number of terms (n).
To derrive this, we use the formula:
An=A1(r)^(n-1)
We plug in the given information...
324=4(3)^n-1
we can then split the exponents into n and -1
324=4(3)^n(3)^-1
Using our calculator, we see that this can be simplified into
324=1.333(3)^n
243.06=3^n
Then we use logarithms to find n
log(base 3)243.06=n
Use change of base formula
we can derive that n=5

Now, we use the finite geometric sum formula
Sn=A1(1-r^n)/(1-r)
Plug in the information we know
Sn=4(1-3^5)/(1-3)
Sn=4(-242)/-2
Sn=-2(-242)
Sn=484