Find the number of two digit numbers which is divisible by 7.
Last updated date: 16th Mar 2023
•
Total views: 305.1k
•
Views today: 5.85k
Answer
305.1k+ views
Hint: To find the number of two digit numbers which is divisible by 7, we need to form an arithmetic progression with common difference as 7. Then we will find the ${{n}^{th}}$ term of this series which will be the highest two digit number that could be a multiple of 7. Then, we use the formula-
${{a}_{n}}$= a + (n-1) d
${{a}_{n}}$= ${{n}^{th}}$ term of this series
a = first term of the series
n = number of terms in the series
d= common difference (7 in this case)
Complete step-by-step solution:
Thus, to proceed with the above problem (to find the appropriate arithmetic series), we first find the ${{n}^{th}}$ term of this series. The ${{n}^{th}}$ term of the series would be the highest two digit number which is a multiple of 7. To find this number, we divide by 100 by 7. Doing so, we get 14 as the quotient and 2 as the remainder. Now, to get this number we subtract the remainder (that is 2) from 100 to get the ${{n}^{th}}$ term of the series. We get, 100 - 2 = 98.
The next step would be the first term of the series. This term would clearly be 14. This is because it is the smallest two digit number that is divisible by 7.
We have, the first term, a = 14 and ${{n}^{th}}$ term, ${{a}_{n}}$=98. For arithmetic progression, we have the formula-
${{a}_{n}}$= a + (n-1) d
Where, n is the required number of terms in the series and d is the common difference (which is 7 in this case)
98 = 14 + 7(n-1)
7(n-1) = 84
n-1=12
n=13
Hence, the required number of terms is 13.
Note: Another technique to arrive at the answer is to divide 100 by 7. We get 14 as the quotient. This implies that the terms are 7, 14, …, 98 (which are 14 terms). However, we have to exclude 7 from the series since it is a single digit number. Thus, the number of terms are 14-1=13.
${{a}_{n}}$= a + (n-1) d
${{a}_{n}}$= ${{n}^{th}}$ term of this series
a = first term of the series
n = number of terms in the series
d= common difference (7 in this case)
Complete step-by-step solution:
Thus, to proceed with the above problem (to find the appropriate arithmetic series), we first find the ${{n}^{th}}$ term of this series. The ${{n}^{th}}$ term of the series would be the highest two digit number which is a multiple of 7. To find this number, we divide by 100 by 7. Doing so, we get 14 as the quotient and 2 as the remainder. Now, to get this number we subtract the remainder (that is 2) from 100 to get the ${{n}^{th}}$ term of the series. We get, 100 - 2 = 98.
The next step would be the first term of the series. This term would clearly be 14. This is because it is the smallest two digit number that is divisible by 7.
We have, the first term, a = 14 and ${{n}^{th}}$ term, ${{a}_{n}}$=98. For arithmetic progression, we have the formula-
${{a}_{n}}$= a + (n-1) d
Where, n is the required number of terms in the series and d is the common difference (which is 7 in this case)
98 = 14 + 7(n-1)
7(n-1) = 84
n-1=12
n=13
Hence, the required number of terms is 13.
Note: Another technique to arrive at the answer is to divide 100 by 7. We get 14 as the quotient. This implies that the terms are 7, 14, …, 98 (which are 14 terms). However, we have to exclude 7 from the series since it is a single digit number. Thus, the number of terms are 14-1=13.
Recently Updated Pages
Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

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

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE
