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