2016-09-24 22:19:51
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.
2016-09-25 02:10:27

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