Five numbers are in A.P.,whose sum is 25 and | vedclass

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

Question

(C) Let the five numbers in $A.P.$ be $(a-2d, a-d, a, a+d, a+2d)$.Sum $= (a-2d) + (a-d) + a + (a+d) + (a+2d) = 5a = 25$,so $a = 5$.The numbers are $(5

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(C) Let the five numbers in $A.P.$ be $(a-2d, a-d, a, a+d, a+2d)$.Sum $= (a-2d) + (a-d) + a + (a+d) + (a+2d) = 5a = 25$,so $a = 5$.The numbers are $(5-2d, 5-d, 5, 5+d, 5+2d)$.The product is $(5-2d)(5+2d)(5-d)(5+d)(5) = 2520$.$(25-4d^2)(25-d^2) = 504$.$625 - 25d^2 - 100d^2 + 4d^4 = 504$.$4d^4 - 125d^2 + 121 = 0$.Let $x = d^2$,then $4x^2 - 125x + 121 = 0$.$(4x - 121)(x - 1) = 0$,so $d^2 = 1$ or $d^2 = \frac{121}{4}$.If $d^2 = 1$,$d = \pm 1$,the terms are $(3, 4, 5, 6, 7)$ or $(7, 6, 5, 4, 3)$,none of which is $-\frac{1}{2}$.If $d^2 = \frac{121}{4}$,$d = \pm \frac{11}{2}$.For $d = \frac{11}{2}$,the terms are $(5-11, 5-5.5, 5, 5+5.5, 5+11) = (-6, -0.5, 5, 10.5, 16)$.Since $-\frac{1}{2}$ is present,this is the correct sequence.The greatest number is $16$.

Five numbers are in $A.P.$,whose sum is $25$ and product is $2520$. If one of these five numbers is $-\frac{1}{2}$,then the greatest number amongst them is

Similar Questions

The sum of all two-digit numbers which,when divided by $4$,yield unity as a remainder is:

Let $G$ be the geometric mean of two positive numbers $a$ and $b,$ and $M$ be the arithmetic mean of $\frac{1}{a}$ and $\frac{1}{b}.$ If $\frac{1}{M}:G$ is $4:5,$ then $a:b$ can be

There are two such pairs of non-zero real values of $a$ and $b$,i.e.,$(a_1, b_1)$ and $(a_2, b_2)$,for which $2a+b, a-b, a+3b$ are three consecutive terms of a $G.P.$. Then the value of $2(a_1b_2 + a_2b_1) + 9a_1a_2$ is-

The sum of the infinite series $\frac{1}{9} + \frac{1}{18} + \frac{1}{30} + \frac{1}{45} + \frac{1}{63} + ..........\infty$ is equal to :-

If $\sum_{r=1}^{n}r^3 - \sum_{p=1}^{n} \sum_{m=1}^{p} \sum_{r=1}^{m} 1 = 80$,then the possible value of $n$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module