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.

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