Question

What is the sum of a 6-term geometric series if the first term is 21 and the last term is 352,947?

Answer 1

so it means a_1=21
and
a_6=352947
you have:
\[\LARGE Sn=a_1\cdot {1-r^n \over 1-r }\]
but you first need to find
r
so here we go:
\[\LARGE a_n=a_1\cdot r^{n-1}\]
\[\LARGE a_6=21\cdot r^{6-1}\]
\[\LARGE 352947=21\cdot r^5\]
\[\LARGE {352947\over 21 }= r^5\]
\[\LARGE 16807= r^5\]
now find here r ... I can't do it without calculator :(
as soon as you do it.
substitute here:
\[\LARGE Sn=a_1\cdot {1-r^n \over 1-r }\]
\[\LARGE S_6=a_1\cdot {1-r^6 \over 1-r }\]
Good Luck! :)

Answer 2

so is 16807 r?