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 $A.P.$ be $A_1, A_2, A_3, A_4$.Given $A_1 + A_4 = 8$ $(i)$ and $A_2 	imes A_3 = 15$ $(ii)$.In an $A.P.$,the sum of terms

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(D) Let the four numbers in $A.P.$ be $A_1, A_2, A_3, A_4$.Given $A_1 + A_4 = 8$ $(i)$ and $A_2 	imes A_3 = 15$ $(ii)$.In an $A.P.$,the sum of terms equidistant from the beginning and end is constant,so $A_2 + A_3 = A_1 + A_4 = 8$ $(iii)$.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 $A_2 = 3$ or $A_2 = 5$.If $A_2 = 3$,then $A_3 = 5$. Since $A_2 = \frac{A_1 + A_3}{2}$,we have $A_1 = 2A_2 - A_3 = 2(3) - 5 = 1$.Then $A_4 = 8 - A_1 = 7$.The series is $1, 3, 5, 7$.The least number of the series 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

If for an arithmetic progression $S_{2n} = 2S_n$,then $S_{3n} / S_n = \dots$

The sum of all those terms of the arithmetic progression $3, 8, 13, \ldots, 373$ which are not divisible by $3$ is equal to $.......$.

The arithmetic mean of the nine numbers in the given set $\{9, 99, 999, \dots, 999999999\}$ is a $9$-digit number $N$,all whose digits are distinct. The number $N$ does not contain the digit:

Different $A.P.$s are constructed with the first term $100$,the last term $199$,and integral common differences. The sum of the common differences of all such $A.P.$s having at least $3$ terms and at most $33$ terms is:

Suppose that the number of terms in an $A.P.$ is $2k$,where $k \in N$. If the sum of all odd-positioned terms of the $A.P.$ is $40$,the sum of all even-positioned terms is $55$,and the last term of the $A.P.$ exceeds the first term by $27$,then $k$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module