Question

please koi solve kardo ________
topic ( arithmetic progression)​

Answer 1

So here the number of the marked house is $x.$

Sum of numbers of houses preceding the marked house will be,

$\longrightarrow S_1=1+2+3+\,\dots\,+(x-1)$

Here the no. of terms is $\dfrac{x-1-1}{1}+1=x-1.$ So,

$\longrightarrow S_1=\dfrac{x-1}{2}\left(1+x-1\right)$

$\longrightarrow S_1=\dfrac{x(x-1)}{2}$

and that of numbers of houses succeeding the marked house will be,

$\longrightarrow S_2=(x+1)+(x+2)+(x+3)+\,\dots\,+49$

Here the no. of terms is $\dfrac{49-(x+1)}{1}+1=49-x.$ So,

$\longrightarrow S_2=\dfrac{49-x}{2}\left(x+1+49\right)$

$\longrightarrow S_2=\dfrac{(49-x)(50+x)}{2}$

Given that both these are equal. So,

$\longrightarrow S_1=S_2$

$\longrightarrow\dfrac{x(x-1)}{2}=\dfrac{(49-x)(50+x)}{2}$

$\longrightarrow x(x-1)=(49-x)(50+x)$

$\longrightarrow x^2-x=2450-x-x^2$

$\longrightarrow 2x^2=2450$

$\longrightarrow\underline{\underline{x=35}}$

Hence 35 is the answer.

Answer 2

Answer:

see my ques. apne GF ka pic lga diye. aur bta diye kyu rhegi mere saath. dekho