What is the average of all multiples of 10 from 2 to 198?

SOLUTION

Data:

Range: 2 to 198

Multiples of 10 are 10, 20, 30 ..... 190

Since the numbers are in Arithmetic progression:

First term = a = 10, 

Last term = tn= 190

Difference = d = 20 - 10 = 10

number of terms = n

Sum = S_n

Formula:

tn = a + (n - 1)d

Sn = \(\frac{n(a + t_n)}{2}\)

Calculation:

190 = 10 + (n - 1) 10

n = 19

Sn = \(\frac{19(10 + 190)}{2} = 1900\)

Average = \(\frac{1900}{19} = 100\)