Question

I am thinking of n consecutive positive integers, the smallest of which is m. What formula represents the largest of these integers?

Answer 1

Answer:

$m+n-1$

Step-by-step explanation:

I am thinking of n consecutive positive integers. The smallest of these numbers is m.

So,

• $a_1=m$ - the first number,
• $a_2=m+1$ - the second number,
• $a_3=m+2$ - the third number,
• ...
• $a_n=m+(n-1)=m+n-1$ - the nth number.

The list of n consecutive positive integers is

$m, \ m+1,\ m+2,\ m+3, \ ... ,\ m+n-1$

The largest integer is $m+n-1$

Answer 2

Answer:

$a_n=m+n-1$

Step-by-step explanation:

We are given that n consecutive integers.

Smallest positive integer=m

We have to find the formula which represents the  largest positive integer of given integers.

Suppose we have n positive consecutive integers

First integer=m

Second positive integer=m+1

Third integer=m+2

:

:

:

$d_1=m+1-m=1$

$d_2=m+2-m-1=1$

Difference between  consecutive integers are constant. It means it is in A.P

nth term of AP is given by

$a_n=a+(n-1)d$

Substitute the value

$a_n=m+(n-1)$

$a_n=m+n-1$

Hence, the formula that represents the largest integer of given integers is given by

$a_n=m+n-1$