# Sequence and series - Arithmetic mean question have been breaking my head

## Homework Statement

Two consecutive numbers from 1,2,3.....n are removed A.M of remaining numbers is 105/4. Find n and those numbers removed .

## Homework Equations

Answer

n = 50
those numbers are 7 and 8

## The Attempt at a Solution

I solved this question like a few weeks ago but now it escaped my brain I have no idea how .. and I am so annoyed now you know how it feels right?
Ok so heres what I got
The A.M of the total numbers would be
n(n+1) / 2 / n

that gives (n+1)/2

now what we get after removing the numbers
let the numbers be x and x+1
therefore their sum = 2x+1

now A.M after removing numbers

n(n+1)/2 - (2x+1) / (n-2) = 105/4

heres one I am not able to figyre out another relation PLease help somebody

## Answers and Replies

eumyang
Homework Helper
Multiply both sides by 2(n-2).
$$\frac{\frac{n(n+1)}{2} - (2x+1)}{n - 2} \cdot 2(n - 2) = \frac{105}{4} \cdot 2(n - 2)$$
Rearrange and you'll find yourself with a quadratic in n. Pretend for a moment that x is a constant, and solve for n using the quadratic formula. Then you'll need to guess-and-check some values of x to make the discriminant a perfect square.