Question

The four arithmetic mean between $3$ and $23$ are

• A. $5,9,11,13$
• B. $7,11,15,19$
• C. $7,11,15,22$
• D. $7,15,19,21$

Answer 1

The correct option is A $5,9,11,13$

A] Let 4 arithmetic means be $a^1,a^2,a^3,a^4$

A.P is $3,a^1,a^2,a^3,a^4,23$

t6 = 23

$\Rightarrow a+(6-1)d=23$

$\to 3+5d=23$

$\Rightarrow 5d=20$

$\therefore$ d=4

$\therefore a^1=3+4=7$

$a^2=7+4=11$

$a^3=11+4=15$

$a^4=15+4=19$