1. The document contains 3 problems about determining the number of 2-digit and 3-digit numbers divisible by 3 and 7. 2. For the 2-digit numbers divisible by 3, it is shown that there are 30 such numbers through setting up and solving an equation for the general nth term of an arithmetic progression. 3. Similarly for the 3-digit numbers divisible by 7, it is determined that there are 128 such numbers.

1. sums G.U.H.S
YELLAGONDAPALAYA
ON LINE
Arithmetic
Progression
Vidyagamma

2. [1] ಎರಡು ಅಂಕಿಗಳ ಎಷ್ುು? ಸಂಖ್ಯೆಗಳು 3 ರಂದ ಭಾಗಿಸಲ್ಪಡುತದಯ?
ಪರಹಾರ: 12, 15, 18, …………99
ಇದು ಸಮಾಂತರ ಶಯರೇಢಿಯೇ ? ಹೌದು ಸಮಾಂತರ ಶಯರೇಢಿ , ಇಲ್ಲಿ,
a = 12, d = 3 , an = 99
ಸೂತರ an = a + ( n – 1 ) d ,
99 = 12 + ( n – 1 ) 3 ,
i.e., 99 – 12 = ( n – 1 ) 3 ,
i.e., 87 = (n – 1) 3 ,
i.e., 87 = 3n – 3 ,
i.e., 87 + 3 = 3n
3n = 90
n =
90
3
n = 30
ಎರಡು ಅಂಕಿಗಳ ಎಷ್ುು?
ಸಂಖ್ಯೆಗಳು -- ರಂದ
ಭಾಗಿಸಲ್ಪಡುತದಯ?
[a] 4
[b] 5
[c] 6
[d] 7
[e] 8
ಆದದರಂದ ಎರಡು ಅಂಕಯಗಳ 30 ಸಂಖ್ಯೆಗಳು 3 ರಂದ ಭಾಗಿಸಲ್ಪಡುತೆಯ

3. [2] ಎರಡು ಅಂಕಿಗಳ ಎಷ್ುು? ಸಂಖ್ಯೆಗಳು 3 ರಂದ ಭಾಗಿಸಲ್ಪಡುತದಯ? [ ಪರ್ಾಾಯ ವಿಧಾನ ]
ಪರಹಾರ: 12, 15, 18, …………99
ಇದು ಸಮಾಂತರ ಶಯರೇಢಿಯೇ ? ಹೌದು ಸಮಾಂತರ ಶಯರೇಢಿ , ಇಲ್ಲಿ,
a = 12, d = 3 , an = 99
ಸೂತರ an = a + ( n – 1 ) d ,
99 = 12 + ( n – 1 ) 3 ,
i.e., 99 – 12 = ( n – 1 ) 3 ,
i.e., 87 = (n – 1) 3 ,
i.e., ( n – 1 ) =
87
3
( n – 1 ) = 29
n = 29 + 1
n = 30
ಎರಡು ಅಂಕಿಗಳ ಎಷ್ುು?
ಸಂಖ್ಯೆಗಳು -- ರಂದ
ಭಾಗಿಸಲ್ಪಡುತದಯ?
[a] 4
[b] 5
[c] 6
[d] 7
[e] 8
ಆದದರಂದ ಎರಡು ಅಂಕಯಗಳ 30 ಸಂಖ್ಯೆಗಳು 3 ರಂದ ಭಾಗಿಸಲ್ಪಡುತೆಯ

4. [1] How many two-digits numbers are divisible by 3?
Solutions: The list of two digit numbers divisible by 3 is :
12, 15, 18, …………99
Is this is an A.P? Yes it is , Here, a = 12, d = 3 , an = 99
As an = a + ( n – 1 ) d ,
We have 99 = 12 + ( n – 1 ) 3 ,
i.e., 99 – 12 = ( n – 1 ) 3 ,
i.e., 87 = (n – 1) 3 ,
i.e., 87 = 3n – 3 ,
i.e., 87 + 3 = 3n
3n = 90
n =
90
3
n = 30
How many two-digits
numbers
are divisible by
[a] 4
[b] 5
[c] 6
[d] 7
[e] 8
There are 30 two-digits numbers are divisible by 3

5. [2] How many two-digits numbers are divisible by 3? [ another type]
Formula an = a + ( n – 1 ) d
We have 99 = 12 + ( n – 1 ) 3 ,
i.e., 99 – 12 = ( n – 1 ) 3 ,
i.e., 87 = (n – 1) 3 ,
i.e., ( n – 1 ) =
87
3
( n – 1 ) = 29
n = 29 + 1
n = 30
How many two-digits
numbers
are divisible by
[a] 4
[b] 5
[c] 6
[d] 7
[e] 8
Solutions: The list of two digit numbers divisible by 3 is :
12, 15, 18, …………99
Is this is an A.P? Yes it is , Here, a = 12, d = 3 , an = 99
There are 30 two-digits numbers are divisible by 3

6. [3] ಮೂರು ಅಂಕಿಗಳ ಎಷ್ುು? ಸಂಖ್ಯೆಗಳು 7 ರಂದ ಭಾಗಿಸಲ್ಪಡುತದಯ?
ಪರಹಾರ: 105, 112, 119, …………994
ಇದು ಸಮಾಂತರ ಶಯರೇಢಿಯೇ ? ಹೌದು ಸಮಾಂತರ ಶಯರೇಢಿ , ಇಲ್ಲಿ,
a = 105, d = 7 , an = 994
ಸೂತರ an = a + ( n – 1 ) d ,
We have 994 = 105 + ( n – 1 ) 7 ,
i.e., 994 – 105 = ( n – 1 ) 7 ,
i.e., 889 = (n – 1) 7 ,
i.e., ( n – 1 ) =
889
7
( n – 1 ) = 127
n = 127 + 1
n = 128
ಮೂರು ಅಂಕಿಗಳ ಎಷ್ುು?
ಸಂಖ್ಯೆಗಳು -- ರಂದ
ಭಾಗಿಸಲ್ಪಡುತದಯ?
[a] 4
[b] 5
[c] 6
[d] 9
[e] 8
ಆದದರಂದ ಮೂರು ಅಂಕಯಗಳ 128 ಸಂಖ್ಯೆಗಳು 7 ರಂದ ಭಾಗಿಸಲ್ಪಡುತೆಯ

7. [3] How many three-digits numbers are divisible by 7 ?
Solution: 105, 112, 119, …………994
Is this is an A.P? Yes it is , Here,
a = 105, d = 7 , an = 994
Formula an = a + ( n – 1 ) d ,
We have 994 = 105 + ( n – 1 ) 7 ,
i.e., 994 – 105 = ( n – 1 ) 7 ,
i.e., 889 = (n – 1) 7 ,
i.e., ( n – 1 ) =
889
7
( n – 1 ) = 127
n = 127 + 1
n = 128
How many two-digits
numbers
are divisible by ?
[a] 4
[b] 5
[c] 6
[d] 9
[e] 8
There are 128 three-digits numbers are divisible by 7