Three numbers are in A.P. whose sum is 33 and product is 792 , then smallest number from these numbe

English

Gujarati

Hindi

8. Sequences and Series

easy

Three numbers are in $A.P.$ whose sum is $33$ and product is $792$, then the smallest number from these numbers is

A

$4$

B

$8$

C

$11$

D

$14$

Solution

(a) Suppose that three numbers are $a + d,\;a,\;a – d,$

therefore $a + d + a + a – d = 33$

$ \Rightarrow $$a = 11$

$a(a + d)(a – d) = 792$

$ \Rightarrow $$11(121 – {d^2}) = 792$

$ \Rightarrow $$d = 7$

Then required numbers are $4, 11, 18.$

Hence smallest number is $4.$

Standard 11

Mathematics

Share

Similar Questions

Let $A B C D$ be a quadrilateral such that there exists a point $E$ inside the quadrilateral satisfying $A E=B E=C E=D E$. Suppose $\angle D A B, \angle A B C, \angle B C D$ is an arithmetic progression. Then the median of the set $\{\angle D A B, \angle A B C, \angle B C D\}$ is

normal

(KVPY-2020)

The sum of the numbers between $100$ and $1000$, which is divisible by $9$ will be

easy

Let $a_n$ be a sequence such that $a_1 = 5$ and $a_{n+1} = a_n + (n -2)$ for all $n \in N$, then $a_{51}$ is

normal

If $\frac{a}{b},\frac{b}{c},\frac{c}{a}$ are in $H.P.$, then

medium

In an arithmetic progression, if $S _{40}=1030$ and $S _{12}=57$, then $S _{30}- S _{10}$ is equal to:

medium

(JEE MAIN-2025)