Three number are in A.P. such that their sum | vedclass

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

Question

(b) Let three number of $A.P.$ $a - d,\,a,\,$$a + d$

Sum = $18$, and ${(a - d)^2} + {a^2} + {(a + d)^2} = 58$

$a - d + a + a + d = 18$

$a = 6

Vedclass · Accepted Answer

$11$

Vedclass · Answer

(b) Let three number of $A.P.$ $a - d,\,a,\,$$a + d$

Sum = $18$, and ${(a - d)^2} + {a^2} + {(a + d)^2} = 58$

$a - d + a + a + d = 18$

$a = 6$ and ${(6 - d)^2} + 36 + {(6 + d)^2} = 158$

= $36 + {d^2} + 36 + {d^2} = 122$

$ = 2{d^2} + 72 = 122$

$ = 2{d^2} = 50$

==> $d = 5$.

Hence Numbers are $1, 6, 11$,

$i.e.$ maximum number is $11$.

Three number are in $A.P.$ such that their sum is $18$ and sum of their squares is $158$. The greatest number among them is

Similar Questions

The income of a person is $Rs. \,3,00,000,$ in the first year and he receives an increase of $Rs.\,10,000$ to his income per year for the next $19$ years. Find the total amount, he received in $20$ years.

If the first term of an $A.P.$ is $3$ and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first $20$ terms is equal to

The roots of the quadratic equation $3 x ^2- px + q =0$ are $10^{\text {th }}$ and $11^{\text {th }}$ terms of an arithmetic progression with common difference $\frac{3}{2}$. If the sum of the first $11$ terms of this arithmetic progression is $88$ , then $q-2 p$ is equal to_______

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

Given that $n$ A.M.'s are inserted between two sets of numbers $a,\;2b$and $2a,\;b$, where $a,\;b \in R$. Suppose further that ${m^{th}}$ mean between these sets of numbers is same, then the ratio $a:b$ equals