Find p

Algebra Level 3

The trees of a row of a garden are numbered consecutively from 1 to 49. There is a value of P such that the sum of the numbers of trees preceding the tree numbered P is equal to the sum of the numbers of the trees following it, then the value of P is.....

28 25 22 35

Ojasee Duble by Ojasee Duble , 19, India

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1 solution

Aaryan Maheshwari
Dec 14, 2017

Sum of the first n n natural numbers is n ( n + 1 ) 2 \dfrac{n(n+1)}{2} , and sum of the terms of an AP is n 2 ( a + l ) \dfrac{n}{2}(a+l) .

So, from question, ( p − 1 ) p 2 = 49 − p 2 × ( p + 1 + 49 ) \dfrac{(p-1)p}{2}=\dfrac{49-p}{2}\space \times\space (p+1+49) p ( p − 1 ) = ( 49 − p ) ( p + 50 ) p(p-1)=(49-p)(p+50) Solving the equation, ⇒ ∴ p = 35 . \Rightarrow\space \therefore\space \boxed{p=35}.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Thanks for the solution! :) Btw, are you 12 or 36 yr old?

Ojasee Duble - 3 years, 5 months ago

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i m 12 Its my father's id. ;)

Aaryan Maheshwari - 3 years, 5 months ago

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