Respuesta :

we know that
the formula of the arithmetic series  is
Sn=n[2(a1) + (n - 1)d]/2 
where
Sn=80
n=20
d=2
a1=?
then
80=20*[2*a1+19*2]/2----------------> 
160=[40*a1+760]
160=[40*a1+760]----------> a1=(160-760)/40------------> a1=-15

the answer is
a1=-15

To solve this, we are going to use the standard formula for arithmetic series [tex]S _{n} = \frac{n}{2} [2a_{1} +(n-1)d][/tex]
where:
[tex]S_{n} [/tex] is the sum of the arithmetic sequence 
[tex]n[/tex] is the number of terms 
[tex]d[/tex] is the difference 
[tex]a_{1} [/tex] is the first term
From our problem we know that [tex]S_{n} =80[/tex], [tex]n=20[/tex], and [tex]d=2[/tex]. Lets replace those values in our formula to find [tex]a_{1} [/tex]:
[tex]80= \frac{20}{2} [2a_{1} +(20-1)2][/tex]
[tex]80=10(2a_{1} +38)[/tex]
[tex]80=20a_{1} +380[/tex]
[tex]20a_{1} =-300[/tex]
[tex]a_{1} = \frac{-300}{20} [/tex]
[tex]a_{1} =-15[/tex]

We can conclude that the first term [tex]a_{1} [/tex] of the arithmetic series is [tex]-15[/tex] 
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