What is the number of digits between 100 and 1000 divisible by 13?
Answers
Here a (first term)=105
d (common difference)=7
an (last term)=994
an=a+(n-1)d
994=105+(n-1)7
994=105+7n-7
994=98+7n
994-98=7n
896=7n
n=896÷7
n=128
There are 128 numbers in between 100 and 1000 which are divisible by 7.
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Answer:
There are 69 numbers between 100 & 1000 which are divisible by 13
Step-by-step explanation:
- 100 ÷ 13 = 7 with a remainder 9.
100 + (13 - 9) = 100 + 4 = 104.
So, the number immediate after 100 which is divisible by 13 is 104.
- 1000÷13 = 76 has 12 as reminder
1000–12=988
So, 998 is the number just before 1000 which is divisible by 13.
- Hence the sequence is:
104,117,.........,988( let there are n terms).
So, the final term 988 = 104 + (n−1)13
⇒(n−1)13 = 988 - 104
⇒ 13n - 13 = 884
⇒ 13n = 884 + 13
⇒ 13n = 897
⇒ n = 897 ÷ 13 = 69
n = 69
So, there are 69 numbers between 100 & 1000 which are divisible by 13.
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