Three consecutive multiple of 7 would 7x,7x+7,7x+21
Answers
Answer:
Three consecutive multiple of 7 will be 7x, 7 (x + 1) and 7 (x + 2)
Step-by-step explanation:
Please mark my answer as BRAINLIEST.
CONSECUTIVE MULTIPLES OF A NUMBER
To find out the consecutive multiples of any number, we need to first understand, what are consecutive numbers.
Consecutive Numbers :- The numbers which follow each other without any gap, i.e., in a continuous order are known as consecutive numbers.
Eg. :- 1,2,3 ... or 5,6,7,8 ... and so on.
Consecutive multiples of a number :- The numbers which occur in a particular table consecutively without any gap are known as consecutive multiples of that number.
Eg. :- Consecutive multiples of 2 are 2,4,6,8... Consecutive multiples of 5 are 5,10,15,20 ... and so on.
When we are unaware of consecutive multiples of a certain number, we take a variable and take its consecutive's to find the consecutive multiples.
For eg. :- Let us take a variable x,
Its consecutive's will be x+1, x+2, x+3 and so on.
Similarly, in order to find consecutive multiples of 7
It will be as follows :-
7x, 7(x+1), 7(x+2), 7(x+3) and so on.
On opening the brackets, it will be :-
7x, 7x+7, 7x+14, 7x+21 and so on.
In the question, you missed 7x+14 term which is a must term for finding a consecutive multiple as per the series given.
Let us now check, how these questions work :-
Q. The sum of three consecutive multiples of 7 is 84. Find the multiples.
Ans. Let the three consecutive multiples be 7x, 7(x+1), and 7(x+2)
ATQ,
7x + 7x + 7 + 7x + 14 = 84
21x + 21 = 84
21 (x + 1) = 84
x + 1 = 84/21
x + 1 = 4
x = 4 - 1
x = 3
We have now got the value of x. Substitute this value in the consecutive multiples to find the actual value of multiples.
- 1st Multiple = 7x = 7*3 = 21
- 2nd Multiple = 7(x+1) = 7(3+1) = 7*4 = 28
- 3rd Multiple = 7(x+2) = 7(3+2) = 7*5 = 35
⇒ The three consecutive multiples of 7 whose sum is 84 are :- 21, 28, 35.