# 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"#

#â€¢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#