Question

What is the arithmetic mean of first 8 multiples of 13?
1. 55.4
2. 58.5
3. 72.5
4. 65.5 

Answer 1

Correct Answer - Option 2 : 58.5

Given:

8 multiples of 13 

Formula Used:

Arithmetic mean = Sum of terms/Number of terms 

Sum of an arithmetic progression = (number of terms/2) × ( first term + last term)

n^th term of an Arithmetic progression = first term + (n – 1) × common difference

Common difference = second term – first term

Calculation:

multiple of 13 ⇒ common difference = 13

First term = 13

8^th term = 13 + (8 – 1) 13

⇒ 8^th term = 13 + 91

⇒ 8^th term = 104

Sum of arithmetic progression = (8/2) × (13 + 104)

⇒ 4 × 117

⇒ 468

Arithmetic mean = 468/8

⇒ 58.5

∴ Arithmetic mean of first 8 multiples of 13 is 58.5