Question

Find the sum of all the multiples of 11 between 100 and 300

Answer 1

110, 121, 132, ... 297 are numbers between 100 and 300 which are divisible by 11.

110, 121, 132, ... 297 form an AP

FORMULA USED

aₙ = a + ( n - 1 ) d

Where,

aₙ = The last term

a = The first term

d = Common difference

n = Number of terms

Here,

a = 110

aₙ = 297

d = 11

n = ?

$\implies 297 = 110 + (n-1)11\\\implies 297-110 = 11(n-1)\\\implies 187 = 11(n-1)\\\implies 77 = n-1\\\implies n = 77+1\\\implies n = 78$

Therefore, there are a total of 78 terms

Now,

Sₙ = n/2 (a + aₙ)

$= \dfrac{78}{2} (110+297)$

$=39 (407)$

$=\boxed{\boxed{\bold{15873}}}}}}$

                                                               

Answer 2

Answer:

Sum of all the multiples of 11 between 100 and 300 is 15,951

Step-by-step explanation:

Hello!

110+121+...........................+257 In an A.P

aₙ = a + ( n - 1 ) d

Here,

a = 110

aₙ = 297

d = 11

n = ?

297 = 110 + (n-1)11

297-110 = 11(n-1)

187 = 11(n-1)

77 = n-1

n = 77+1

n = 78

⟹297=110+(n−1)11

⟹297−110=11(n−1)

⟹187=11(n−1)

⟹77=n−1

⟹n=77+1

⟹n=78

Therefore, there are a total of 78 terms

Now,

Sₙ = n/2 (a + aₙ)

= {78}{2} (110+297)

=39 (110+297)

=39 (407)

=39(407)

=15,951

Hence, Sum of all the multiples of 11 between 100 and 300 is 15,951

I hope you are understand the problem