Question

Find the sum of a 10-term geometric sequence when the first term is 3 and the last term is 59,049 and select the correct answer below.

pleeaaassseeee someone help

Answer 1

we have to apply the subsequent formula:
\[\Large {a_{10}} = {a_1}{q^9}\]
from which we have:
\[\Large q = \sqrt[9]{{\frac{{{a_{10}}}}{{{a_1}}}}}\]
where q is the constant of the geometric sequence.
What is the value of q?

Answer 2

hint:
\[\Large q = \sqrt[9]{{\frac{{{a_{10}}}}{{{a_1}}}}} = \sqrt[9]{{\frac{{59049}}{3}}} = ...?\]

Answer 3

the requested sum S, is given by the subsequent formula:
\[\Large S = {a_1}\frac{{1 - {q^9}}}{{1 - q}} = ...?\]
where a_1=3, namely is the first term of your geometric sequence

Answer 4

note that once you find \(q\) you don't have to compute \(q^n\) again and you can just determine the sum using $$S=\frac{a_{10}-a_1}{q-1}$$

Answer 5

so whats the answer?