Answer
$6080$
Work Step by Step
We can see that there are $80$ terms and these terms are part of an arithmetic sequence, so we have:
$a_1=(2)(1)-5=-3 \\ a_{80}=(2)(80)-5=155$
There is a constant difference between the terms
: $d=a_{n+1}-a_n=2(n+1) -5 -(2n-5)=2n+2-5-2n+5-2n+5=2$
The sum of the first $n$ terms of an arithmetic sequence is given by:
$S_{n}= \dfrac{n}{2}\left(a_{1}+a_{n}\right) ..(1)$
Now, we plug in the above data into Equation-1 to obtain:
$S_{80}= \dfrac{80}{2}[-3+155] \\=(40)(152) \\= 6080$
Therefore, the sum of the arithmetic sequence is: $6080$.
