Page 8 - Arithmetic

Worked Example 6
Find the sum of all even numbers between 1 and 61.
Solution:
The A.P. series of even numbers = 2, 4, 6, 8...,60 First term = 2
Last term = 60
Let the A.P contain ‘n’ terms
2 + (n -1) 2 = 60 2(n – 1) = 58
n – 1 = 29
n = 30
Sn = 𝑛 [first term + last term] 2
= 30 [2+ 60] 2
= 15 × 62 = 930
Geometric progression
It’s a series of numbers such that the ratio between the two consecutive terms is a constant ratio. The constant term is called the common ratio and is denoted by ‘r’. Also, the first term of G.P. is denoted by ‘a’.
REMEMBER:
A G.P. series is denoted by
234n a, ar, ar , ar , ar ...ar
The nth term of any G.P. is given by:
Tn =ar(n–1)
Sum of the terms of G.P. = Sn 1−𝑟 =
𝑎(1−𝑟𝑛)
Worked Example 7
Find the 8th term of the series 1, 3, 9, 18,...
Solution:
a =1 n =8
r=3=9=3 13
Tn =ar(n–1)
Tn = 1 × 3(8-1) = 2187
Page 7 of 55
Arithmetic Concept