Question

Find out the Şum
What is the sum of all numbers between 100 and
1000 which are divisible by 14?​

Answer 1

Step-by-step explanation:

we can find out the sum using arithmetic progression formulas. I’m going to tell you that formulas:

a) Tn=a+(n-1)d

where,

Tn= nth term

a= first term of arithmetic sequence

n= number of terms

d= common difference

b) Sn=n/2 *(a+l)

where,

Sn= sum of n terms in arithmetic sequence

n= number of terms in the sequence

a= first term of the sequence

l= last term of the sequence

So, come to our question we have to find the sum of numbers in between 100 -1000, which can be divided by 14.

so the numbers that are divisible by 14 in between 100–1000:

112,126,140,…..,+966+980+994

now see this it is an arithmetic sequence.

which has,

Tn=994

a=112

d=14

n=?

by using formula (a) written above you can find out the number of terms. by calculating you will get:

n=64 terms

So, now by using the formula (b) we can find out the sum of 64 terms. In formula (b) the data as follow:

Sn=?

n=64

a=112

l=994

by putting values we get the sum of numbers in between 100 -1000, which can be divided by 14 is 35392. (S64 means sum of 64 terms)

S64= 35392 Answer.