Question

Insert three arithmetic means between 4 and 12.

• A. 7,9,11
• B. 6,8,10
• C. 5,8,11
• D. 4,8,12

Answer 1

The correct option is B

6,8,10

When we have to insert 'n' arithmetic means between two numbers 'a' and 'b', then the common difference is given by $d=\frac{(b-a)}{(n+1)}$.
The resulting AP is given by a, a+d, a+ (2$\times$d),...., a+(n$\times$d) ,b.
Given,

a = 4, b = 12, n = 3.
Therefore $d=\frac{(12-4)}{(3+1)}=2$
$\therefore$The resulting sequence is 4, 6, 8, 10, 12
$\Rightarrow$The arithmetic means are 6, 8, 10.