Question

find the sum of all numbers between 100 and 200 which are divisible by 5​

Answer 1

Step-by-step explanation:

The numbers which are divisible by 7 between 100 and 200 are 105,112,119,126,...,196

The given series is in A.P. Since, the difference between the consecutive terms is constant. i.e., 11−105=119−112=...=7

The first term a=105

The common difference d=7

The last term a

n

=196

⟹a+(n−1)d=196

⟹105+(n−1)7=196

⟹(n−1)7=91

⟹n−1=13

⟹n=14

Therefore the sum the terms is S

n= 2

n (a+a n)

⟹S

n =214

(105+196)

⟹S

n=7(301)=2107

Therefore, the sum of all the numbers between 100 and 200 which are divisible by 7 is 2107

Answer 2

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The series as per question is 102,108, 114,........., 198.

Which is an A.P,

Given :-

a = 102

d = 6

l = 198

198 = 102 + ( n - 1 )6

96/6 = n - 1

n = 17

S17 = n/2(a+l)

S17 = 17/2( 102 + 198 )

S17 = 17/2 × 300

= 17 × 150

= 2550