Question

i) Complete the following activity to find the sum of all natural numbers between
1 and 81 divisible by 6.
The natural numbers between 1 and 81 divisible by 6 are 6, 12, 18, ..., 78.
Here, a=1,=6, d=6, 1,= 78, n=?, S=?
.. (Formula)
.. 78=6+
.. (Substituting the values)
... 78
78=0
..n=13
S.-
(Formula)
S
13
2
SO​

Answer 1

78=a+(n-1)d

78=6+(n-1)6

78-6=6n-6

72+6=6n

78=6n

78/6=n

13=n

A/Q

S13=n/2(2a+(n-1)d)

=13/2(2*6+(13-1)6

=13/2(12+(12)6

=13/2(12+72)

=13/2(84)

=13*42

=546

Answer 2

546 is the correct answer

Given:

• the sum of all natural numbers between  1 and 81 divisible by 6.

• The natural numbers between 1 and 81 divisible by 6 are 6, 12, 18, ..., 78.
• a=6, d=6, 1,= 78

Explanation:

6,12,18,-,-,-,-,-,-,-,-,78 is the given sequence

a=6, d=6, an= 78

an = a+(n-1)d is the required formula

on substitution,

78 = 6+(n-1) 6

72 = (n-1)6

12 = n-1

n = 13

sum of 13 terms will be,

Sn= n/2 (2a+(n-1)d) on substitution,

s13 = 13/2(12+(13-1)6)

=13/2×(12+72)

=13/2×84

=13×84/2

=13×42

=546

S13 = 546

hence, S13 is 546