Introduction to Product of two consecutive integers:
Consecutive integer is the number after the same number. Let take the a number a and its consecutive number can be said as a + 1.
Example: (4,5), (6,7) (5,6), (21, 22)
Product of two consecutive integers is nothing but multiplication of the number and its consecutive number. Thus the result of the multiplication of the number and its consecutive is called as product of two consecutive integers. In this article, we see about the product of two consecutive integers.
Product of Two Consecutive Integers:
Formula: multiplication of integer and its consecutive
Let take the number as ‘’a’’ and its consecutive is ‘’a + 1’’.
Step 1: Multiplication of the number ‘’a’’ and its consecutive
a * (a + 1) = a + a2
Thus the product of the integer and its consecutive is equal to the sum of the integer and its square of the same integer.
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Example Problems – Product of Two Consecutive Integers:
Example problem 1:
What is the product of the integer 10 and its consecutive?
Solution:
Formula: a * (a + 1) = a + a2
Here a = 10
10 * (10 + 1) = 10 + 102
Square of 10 =100
10 + 100 = 110
Answer: 110
Check the answer:
Step 1: The consecutive integer of 10 is 11
10 * (11) = 110
Therefore the answer is correct.
Example 2:
The product of two consecutive positive integers is 420. Find the integer and its consecutive integer.
Solution: Let take the integer as ‘’a’’ and its consecutive is ‘’a + 1’’
Formula: a * (a + 1) = a + a2
a * (a + 1) = a + a2 = 420
a2 + a - 420 = 0 --- > equation 1
Step 1: Factoring the equation1, we get the integer.
a2 + a - 420 = 0
a2 -20a + 21a - 420 = 0
a (a - 20) + 21 (a - 20) = 0
(a -20) (a + 21) = 0
Possibilities of ‘’a’’ value is
a = 20
a = -21
Note: in given problem the integer is positive. Hence the value of the integer is 20 and its consecutive is 20 +1 = 21
Answer: 20 and 21
Practice Problem – Product of Two Consecutive Integers:
1. What is the product of the integer -5 and its consecutive?
Answer: 20
2. What is the product of the integer 5 and its consecutive?
Answer: 30
Consecutive integer is the number after the same number. Let take the a number a and its consecutive number can be said as a + 1.
Example: (4,5), (6,7) (5,6), (21, 22)
Product of two consecutive integers is nothing but multiplication of the number and its consecutive number. Thus the result of the multiplication of the number and its consecutive is called as product of two consecutive integers. In this article, we see about the product of two consecutive integers.
Product of Two Consecutive Integers:
Formula: multiplication of integer and its consecutive
Let take the number as ‘’a’’ and its consecutive is ‘’a + 1’’.
Step 1: Multiplication of the number ‘’a’’ and its consecutive
a * (a + 1) = a + a2
Thus the product of the integer and its consecutive is equal to the sum of the integer and its square of the same integer.
Stuck on any of these topics word math problem solver, math online tutoring try out some best math website like mathsisfun, mathcaptain.com and math dot com.
Example Problems – Product of Two Consecutive Integers:
Example problem 1:
What is the product of the integer 10 and its consecutive?
Solution:
Formula: a * (a + 1) = a + a2
Here a = 10
10 * (10 + 1) = 10 + 102
Square of 10 =100
10 + 100 = 110
Answer: 110
Check the answer:
Step 1: The consecutive integer of 10 is 11
10 * (11) = 110
Therefore the answer is correct.
Example 2:
The product of two consecutive positive integers is 420. Find the integer and its consecutive integer.
Solution: Let take the integer as ‘’a’’ and its consecutive is ‘’a + 1’’
Formula: a * (a + 1) = a + a2
a * (a + 1) = a + a2 = 420
a2 + a - 420 = 0 --- > equation 1
Step 1: Factoring the equation1, we get the integer.
a2 + a - 420 = 0
a2 -20a + 21a - 420 = 0
a (a - 20) + 21 (a - 20) = 0
(a -20) (a + 21) = 0
Possibilities of ‘’a’’ value is
a = 20
a = -21
Note: in given problem the integer is positive. Hence the value of the integer is 20 and its consecutive is 20 +1 = 21
Answer: 20 and 21
Practice Problem – Product of Two Consecutive Integers:
1. What is the product of the integer -5 and its consecutive?
Answer: 20
2. What is the product of the integer 5 and its consecutive?
Answer: 30
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