If the sum of three numbers of a arithmetic s | vedclass

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

Question

(b) Let three numbers are $a - d,\;a,\;a + d$.

We get $a - d + a + a + d = 15$

$ \Rightarrow $$a = 5$

and ${(a - d)^2} + {a^2} + {(a + d)^2}

Vedclass · Accepted Answer

$3, 5, 7$

Vedclass · Answer

(b) Let three numbers are $a - d,\;a,\;a + d$.

We get $a - d + a + a + d = 15$

$ \Rightarrow $$a = 5$

and ${(a - d)^2} + {a^2} + {(a + d)^2} = 83$

$ \Rightarrow $ ${a^2} + {d^2} - 2ad + {a^2} + {a^2} + {d^2} + 2ad = 83$

$ \Rightarrow $$2({a^2} + {d^2}) + {a^2} = 83$

Putting $a = 5$

$ \Rightarrow $$2(25 + {d^2}) + 25 = 83$

$ \Rightarrow $$2{d^2} = 8$

$ \Rightarrow $$d = 2$

Thus numbers are $3, 5, 7.$

Trick : Since $3 + 5 + 7 = 15$

and ${3^2} + {5^2} + {7^2} = 83$.

If the sum of three numbers of a arithmetic sequence is $15$ and the sum of their squares is $83$, then the numbers are

Similar Questions

Let ${a_1},{a_2},{a_3}, \ldots $ be terms of $A.P.$ If $\frac{{{a_1} + {a_2} + \ldots + {a_p}}}{{{a_1} + {a_2} + \ldots + {a_q}}} = \frac{{{p^2}}}{{{q^2}}},p \ne q$ then $\frac{{{a_6}}}{{{a_{21}}}}$ equals

Let ${T_r}$ be the ${r^{th}}$ term of an $A.P.$ for $r = 1,\;2,\;3,....$. If for some positive integers $m,\;n$ we have ${T_m} = \frac{1}{n}$ and ${T_n} = \frac{1}{m}$, then ${T_{mn}}$ equals

If $a _{1}, a _{2}, a _{3} \ldots$ and $b _{1}, b _{2}, b _{3} \ldots$ are $A.P.$ and $a_{1}=2, a_{10}=3, a_{1} b_{1}=1=a_{10} b_{10}$ then $a_{4} b_{4}$ is equal to

If $A$ be an arithmetic mean between two numbers and $S$ be the sum of $n$ arithmetic means between the same numbers, then

If $\log _{10} 2, \log _{10} (2^x + 1), \log _{10} (2^x + 3)$ are in $A.P.,$ then :-