The four arithmetic means between 3 and 23 ar | vedclass

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

Question

(b) Let four arithmetic means are ${A_1},{A_2},\;{A_3}$ and ${A_4}$.

So $3,\;{A_1},\;{A_2},\;{A_3},\;{A_4},\;23$

$ \Rightarrow $ ${T_6} = 23 = a

Vedclass · Accepted Answer

$7, 11, 15, 19$

Vedclass · Answer

(b) Let four arithmetic means are ${A_1},{A_2},\;{A_3}$ and ${A_4}$.

So $3,\;{A_1},\;{A_2},\;{A_3},\;{A_4},\;23$

$ \Rightarrow $ ${T_6} = 23 = a + 5d$

$ \Rightarrow $ $d = 4$

Thus ${A_1} = 3 + 4 = 7,\;{A_2} = 7 + 4 = 11,\;$

$A_3 = 11+4 =15 ,\, A_4 = 15+ 4=19$

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

Similar Questions

If $\frac{a^{n}+b^{n}}{a^{n-1}+b^{n-1}}$ is the $A.M.$ between $a$ and $b,$ then find the value of $n$.

The mean of the series $a,a + nd,\,\,a + 2nd$ is

If the ${p^{th}},\;{q^{th}}$ and ${r^{th}}$ term of an arithmetic sequence are $a , b$ and $c$ respectively, then the value of $[a(q - r)$ + $b(r - p)$ $ + c(p - q)] = $

If the numbers $a,\;b,\;c,\;d,\;e$ form an $A.P.$, then the value of $a - 4b + 6c - 4d + e$ is

Let $S_{n}$ denote the sum of first $n$-terms of an arithmetic progression. If $S_{10}=530, S_{5}=140$, then $\mathrm{S}_{20}-\mathrm{S}_{6}$ is equal to :