If the first and the last terms of an arithmetic series are 10 and 62, show that the sum of the series varies directly as the number of terms

Answer 1

a=10
a+(n-1)d = 62
10 + nd - d = 62
nd-d=52
n=(52+d)/d or d = 52/(n-1)

sum(n) = (n/2)(2a + (n-1)d)
= (n/2)(20 + (n-1)(52)/(n-1))
= (n/2)(20 + 52)
= (n/2)(72) = 36n

sum(n) = 36n
so sum(n) varies directly as the number of terms