### Types of Questions Consecutive integers

Consecutive integers are the important part of **SAT, ACT, GMAT **and **GRE **Quantitative, based on this topic a variety of questions can be framed, some of those types will be discussed here. Before discussing about types of questions you may expect,let’shave a brief about consecutive integers.

What Consecutive integers are? Well, Consecutive integers are those numbers which follow one an other without skipping; those may be negative and positive including zero, examples are 7, 8, 9,… and ‐2, ‐1, 0, 1, 2, 3, 4, 5… are consecutive integers.

- FINDING NUMBER OF TERMS IN GIVEN RANGE

*Number of terms in a range, inclusive:**(Last Term-First Term) +1*

*Number of terms between: **(Last Term-First Term )-1*

*Example 1: How many integers are there from 5 to 10 inclusive?*

Method: (Last Term – First Term )+1

For above example (10-5)+1=6

5,6,7,8,9,10

** Number of multiples of ‘x’ in a given range: (Last multiple of x -First multiple of x)/** (

**))**

*Common difference*

*+ 1*

* *

Where x is an integer

*Example 2: How many even numbers are there from 128 to 200 inclusive?*

Solution: {(Last multiple of 2-First multiple of 2) ÷ 2} + 1

{(200-128)÷2} +1=37

- FINDING SUM OF CONSECUTIVE INTEGERS

**Sum of terms:** Average of terms *number of terms

Average of terms: (First term +Last term) /2

*Sum of Consecutive numbers in a range: ((First term +Last term)/2 )*number of terms** *

*Example 3:* What is the sum of all integers from 80 to 120, inclusive?

Step 1: Find average of first and last term.

Average = (120+80) ÷2

=100

Step 2: Find the number of terms: 120-80+1= 41.

Step 3: Multiply the mean and number of terms 100×41=4100

**Note**

*Sum of first n consecutive numbers is given by: n (n +1), Where n is the last term*

*2*

*Sum of first n positive even numbers= n (n +1), Where n is the number of even terms**Sum of first n positive odd numbers= n*^{2}, Where n is the number of odd terms*For any set of consecutive integers with an ODD number of items, the sum of all the integers is ALWAYS a multiple of the number of items.*

*Example 4:*9+10+11+12+13=55

In the above example, number of items are 5(odd) so the sum 55, which is multiple of number of items

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