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AkshithaZayn
@AkshithaZayn
June 2021
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Find the sum of number which are divisible by 7 between 100 and 1000
Answers & Comments
Swarup1998
The answer is given below :
The first number (divisible by 7) between 100 and 1000 is 105 and the last number (divisible by 7) between 100 and 1000 is 994.
Let us consider that 994 is the n-th term.
Then,
n-th term = first term + (n - 1)×common difference
=> 994 = 105 + (n - 1)×7
=> 7n - 7 = 994 - 105
=> 7n = 889 + 7
=> 7n = 896
=> n = 128
So, there are 128 numbers (between 100 and 1000) divisible by 7.
So, the sum of the 128 numbers
= n/2 (first number + last number)
= 128/2 (105 + 994)
= 64 × 1099
= 70336
Thank you for your question.
0 votes
Thanks 2
AkshithaZayn
tq :)
Swarup1998
my pleasure
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Answers & Comments
The first number (divisible by 7) between 100 and 1000 is 105 and the last number (divisible by 7) between 100 and 1000 is 994.
Let us consider that 994 is the n-th term.
Then,
n-th term = first term + (n - 1)×common difference
=> 994 = 105 + (n - 1)×7
=> 7n - 7 = 994 - 105
=> 7n = 889 + 7
=> 7n = 896
=> n = 128
So, there are 128 numbers (between 100 and 1000) divisible by 7.
So, the sum of the 128 numbers
= n/2 (first number + last number)
= 128/2 (105 + 994)
= 64 × 1099
= 70336
Thank you for your question.