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,$3, A_1, A_2, A_3, A_4, 23$ are in an arithmetic progression. Here,the first ter

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,$3, A_1, A_2, A_3, A_4, 23$ are in an arithmetic progression. Here,the first term $a = 3$ and the $6^{th}$ term $t_6 = 23$. Using the formula $t_n = a + (n-1)d$: $23 = 3 + (6-1)d$ $23 = 3 + 5d$ $5d = 20$ $d = 4$ Now,calculating 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

Let $x, y, z$ be positive real numbers such that $x + y + z = 12$ and $x^3y^4z^5 = (0.1)(600)^3$. Then $x^3 + y^3 + z^3$ is equal to

If the sum of the first $2n$ terms of the arithmetic progression $2, 5, 8, \dots$ is equal to the sum of the first $n$ terms of the arithmetic progression $57, 59, 61, \dots$,then $n = \dots$

If the $p^{th}$ term of an $A.P.$ is $\frac{1}{q}$ and the $q^{th}$ term is $\frac{1}{p}$,then the sum of its $pq$ terms is:

The sums of $n$ terms of three $A.P.'s$ whose first term is $1$ and common differences are $1, 2, 3$ are ${S_1}, {S_2}, {S_3}$ respectively. The true relation is

If the $m^{th}$ terms of the sequences $63, 65, 67, 69, \dots$ and $3, 10, 17, 24, \dots$ are equal,then $m = \dots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module