Four numbers are in arithmetic progression. T | vedclass

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

Question

(D) Let the four numbers in arithmetic progression be $A_1, A_2, A_3, A_4$.Given that $A_1 + A_4 = 8$ $(i)$ and $A_2 	imes A_3 = 15$ $(ii)$.In an ari

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(D) Let the four numbers in arithmetic progression be $A_1, A_2, A_3, A_4$.Given that $A_1 + A_4 = 8$ $(i)$ and $A_2 	imes A_3 = 15$ $(ii)$.In an arithmetic progression,the sum of terms equidistant from the beginning and the end is constant and equal to the sum of the first and last terms.Therefore,$A_2 + A_3 = A_1 + A_4 = 8$ $(iii)$.From $(ii)$ and $(iii)$,we have $A_2 + \frac{15}{A_2} = 8$,which simplifies to $A_2^2 - 8A_2 + 15 = 0$.Solving the quadratic equation,we get $(A_2 - 3)(A_2 - 5) = 0$,so $A_2 = 3$ or $A_2 = 5$.If $A_2 = 3$,then $A_3 = 5$. If $A_2 = 5$,then $A_3 = 3$.Using the property $A_2 = \frac{A_1 + A_3}{2}$,we find $A_1 = 2A_2 - A_3$.For $A_2 = 3$ and $A_3 = 5$,$A_1 = 2(3) - 5 = 1$. Then $A_4 = 8 - 1 = 7$.The series is $1, 3, 5, 7$. The least number is $1$.

Four numbers are in arithmetic progression. The sum of the first and last term is $8$ and the product of both middle terms is $15$. The least number of the series is

Similar Questions

For $x \in R$,let $[x]$ denote the greatest integer $\le x$. Find the sum of the series $\left[ -\frac{1}{3} \right] + \left[ -\frac{1}{3} - \frac{1}{100} \right] + \left[ -\frac{1}{3} - \frac{2}{100} \right] + \dots + \left[ -\frac{1}{3} - \frac{99}{100} \right]$.

The $4$th term of an $A.P.$ is equal to $3$ times the first term and the seventh term exceeds twice the third term by $1$. Find the first term and the common difference.

If the sum $\frac{3}{1^2} + \frac{5}{1^2 + 2^2} + \frac{7}{1^2 + 2^2 + 3^2} + \dots$ up to $20$ terms is equal to $\frac{k}{21}$,then $k$ is equal to

$0.4\overline{23} = $

Let $a_1, a_2, ......., a_{30}$ be an $A.P.$,$S = \sum_{i=1}^{30} a_i$ and $T = \sum_{i=1}^{15} a_{2i-1}$. If $a_5 = 27$ and $S - 2T = 75$,then $a_{10}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module