The four arithmetic means between 3 and 23 ar | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the four arithmetic means be $A_1, A_2, A_3,$ and $A_4$.Then the sequence $3, A_1, A_2, A_3, A_4, 23$ forms an Arithmetic Progression $(AP)$ w

Vedclass · Accepted Answer

$7, 11, 15, 19$

Vedclass · Answer

(B) Let the four arithmetic means be $A_1, A_2, A_3,$ and $A_4$.Then the sequence $3, A_1, A_2, A_3, A_4, 23$ forms an Arithmetic Progression $(AP)$ with $n = 6$ terms.The $n^{th}$ term of an $AP$ is given by $T_n = a + (n-1)d$.Here,$a = 3$ and $T_6 = 23$.$23 = 3 + (6-1)d$$23 = 3 + 5d$$20 = 5d$$d = 4$Now,we calculate the means:$A_1 = a + d = 3 + 4 = 7$$A_2 = a + 2d = 3 + 8 = 11$$A_3 = a + 3d = 3 + 12 = 15$$A_4 = a + 4d = 3 + 16 = 19$Thus,the four arithmetic means are $7, 11, 15, 19$.

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

Similar Questions

Which one of the following is the most widely accepted method of contraception in India,at present?

What happens when
$(i)$ sodium metal is dropped in water?
$(ii)$ sodium metal is heated in free supply of air?
$(iii)$ sodium peroxide dissolves in water?

If $\frac{dy}{dx} = \frac{xy + y}{xy + x}$,then the solution of the differential equation is

Which plot is the adsorption isobar for chemisorption?

$A$ uniform beam of weight $W$ is attached to a vertical wall by a hinge $H$. The beam is held horizontal by a rope as shown below. Which one of the following best shows the direction of the reaction force $R$ at the hinge?

Vedclass Test Series

Exam Paper Generator

Online Exam Module