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In an arithmetic sequence...

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in an arithmetic series, an = a0+ (n-1) *d
 
that means the nth term is equal to the first term plus n-1 times the common difference.
 
In this case we are told a3=10 and a5=16
 
so:  a3= a+ 2*d =10    => a0= 10-2d     
and      
      a5= a+4*d = 16     => a0= 16-4d
 
so 10-2d = 16-4d => 2d=6 => d=3
 
now you can plug this value of d into any of those equations we got for a0 and find a0.
for example a0= 10-2(3) = 4 so the first term is 4
 
the formula for the sum of the first n terms is:
 
Sn = (n/2)* [2a0+ (n-1)*d]
 
so S20 = (20/2) * [2*4 + (19)*(3)] = 10* [65] = 650