Answer

Verified

346.2k+ views

**Hint:**For solving this question you should know about the arithmetic progression A.P. and if we make the series for it then firstly we will find the first term and then we will find next same terms with a common difference of 7 because the question is asking for the same.

**Complete step by step answer:**

According to our question it is asked to calculate how many numbers there are between 1 and 1000 which when divided by 7 leave the remainder 4.

So, as we know that if any statement is given which shows about a type of a number, how it will be implemented, then we first make the first term which can be generated by the given information and then we find the next terms as a series wise or as an arithmetic progression wise.

So, according to the given statement in question we will evaluate that if we divide a number by 7 then it leaves a remainder 4.

So, we can write, if a number is divided by 7 and the remainder 4, then it must be in the form of \[7k+4\].

Let, \[{{T}_{k}}=7k+4\] from 1 to 1000

First term is ‘4’

And the common difference is ‘7’

And last term is \[\left( l \right)=998\]

\[\begin{align}

& \because l=a+\left( n-1 \right)d \\

& 998=4+\left( n-1 \right)7 \\

& 998=7n-3 \\

& 7n=1001 \\

& n=143 \\

\end{align}\]

So, the total terms are 143.

**Note:**While solving these types of problems you have to mind that you must make your first term with an exact remainder and common difference. And the term must be satisfied with the statement given in the question.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

One cusec is equal to how many liters class 8 maths CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

How many crores make 10 million class 7 maths CBSE

Change the following sentences into negative and interrogative class 10 english CBSE