Find the sum of each of the following series:
(a) 2 + 7 + 12 + +92

Arithmetic SequenceWe can observe that we are adding 5 each time to the numbers, meaning this is an arithmetic sequence with a common difference d=5Explicit RelationWe can establish the relation,u(n)=u⁰+nd

where u(n) is the nth term (any term).

u⁰ is out first term (2)

d is the common difference (5)

u(n)=u⁰+nd92 =2 +5n5n =90n =18This sequence admits 19 terms since we start counting from 0 till 18.SummationS= number of terms/2 ×(u¹⁸+u⁰)

That's ur answer :)