Math, asked by suryakjr2302, 1 year ago

Find the sum of all 3 digit number which are multiple of 7

Answers

Answered by dhruvsh
120
Smallest three digit number divisible by 7 = 105 and the largest = 994
An = 994
A = 105
D = 7 
n= ?
An = A + [ n - 1] D
thus 
994 = 105 + [ n - 1 ] 7
thus by solving further
n = 128

now,
Sn = n/2 [ A + An]

Sn = 128/2 [ 105 + 994]
thus,
Sn = 70336.
Thus the sum of all the three digit numbers divisible by 7 is 70336.
Answered by alia20
36
First three digit term divisible by 7 is 105

Last three digit term divisible by 7 is 994

We know that tn=a+(n−1)dtn=a+(n−1)d

⇒994=105+(n−1)7⇒994=105+(n−1)7

⇒n=128⇒n=128

We know that Sn=n2Sn=n2(l+a)(l+a)

∴∴ The sum of the required series Sn=1282(994+105)Sn=1282(994+105)

=64×1099=70336


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