Question

9. Find the sum of all natural numbers less than 100 which are divisible
by 6.

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Answer 1

The natural numbers less than 100 and divisible by 6 : 6 , 12 , 18 , 24 , ... 96

Using the Arithmetic Progression form
Tn = a + (n - 1) d

a = 6
d = 6

Find the number of terms of AP

96 = 6 + (n - 1) 6

96 = 6 + (6n - 6)

96 - 6 = 6n - 6

90 = 6n - 6

90 + 6 = 6n

96/6 = n

n = 16

Find the Sum of the nth terms = 16

Sn = n/2 ( a + l )

S16 = 16/2 (6 + 96)

S16 = 8 * 102

= 816



Hope it would help