Question #5edfb
2 Answers
See explanation.
Explanation:
So you have a sequence that goes:
3, 8, 13, 18,...
One possibility that I see right away is that
then
If we call the first entry,
and the second entry of sequence,
we can rewrite the first and second entries as follows:
the third entry would be written:
fourth entry:
...
sixty-sixth entry:
We want the sum of
We now notice that we can rewrite these equations as such:
...
Thus the sum can be written:
which can be simplified to:
and even to:
so:
Explanation:
#"the sum to n terms of an arithmetic sequence is"#
#•color(white)(x)S_n=n/2[2a+(n-1)d]#
#"where a is the first term and d the common difference"#
#"here "a=3" and "d=18-13=13-8=8-3=5#
#rArrS_(66)=33[(2xx3)+(65xx5)]#
#color(white)(rArrS_(66))=33(6+325)#
#color(white)(rArrS_(66))=10923#