Find the sum of all the multiples of 11 between 100 and 300
Answers
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 = ?
Therefore, there are a total of 78 terms
Now,
Sₙ = n/2 (a + aₙ)
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