Question

find the sum of natural number less than 100 which are divisible by 7

Answer 1

Natural number less than 100 = 1, 2, 3,..., 99
First natural number which is divisible
by 7 = 7
Therefore, this is 'a' = 7
Common difference 'd' = 7
Last natural number divisible by 7 = 98
Therefore, this is 'an' last natural number
= 98

FIND
Number of natural numbers divisible
by 7 but should be less than 100 = 'n'

FORMULA
an = a + (n - 1)d ............... (1)
SUM 'Sn' = n [a + an] / 2............ (2)

SUBSITUTE VALUES in (1)
98 = 7 + 7(n - 1)
(98 - 7) / 7 = n - 1
91 / 7 = n - 1
13 = n - 1
13 + 1 = n
n = 14
Therefore, number of natural numbers divisible by 7, but are less than 100 = 14

SUBSITUTE 'n' VALUE in (2)
SUM, Sn = [14 (7 + 98)] / 2
Sn = 14 x 105 / 2
Sn = 735

*****Sum of natural numbers less than 100 which are divisible by 7 are 735.