Types of Questions on Consecutive Integers

Last updated on September 28th, 2022 at 04:08 pm

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.


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


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


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


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

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


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


  1. Sum of first n positive even numbers= n (n +1), Where n is the number of even terms
  2. Sum of first n positive odd numbers= n2, Where n is the number of odd terms
  3. 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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