215,147 views
33 votes
33 votes
Find the sum of each of the following series:
(a) 2 + 7 + 12 + ...... +92

User TKTS
by
2.9k points

1 Answer

11 votes
11 votes

Arithmetic Sequence

We can observe that we are adding 5 each time to the numbers, meaning this is an arithmetic sequence with a common difference d=5

Explicit Relation

We 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+nd

92 =2 +5n

5n =90

n =18

This sequence admits 19 terms since we start counting from 0 till 18.

Summation

S= number of terms/2 ×(u¹⁸+u⁰)


s = (19)/(2) * (92 + 2)


s = 9.5(94)


s = 893

That's ur answer :)

User Venca
by
2.5k points