Find the sum of a

To find: the sum of all integers between 84 and 719, which are multiples of 5.

Solution: 


The smallest and largest digits between 84 and 719 which are divisible by 5 is 85 and 715.

So the sequence will be 85,90,........... 715.

 a = 85, d = 5, l = 715


From the formula l=a+(n-1)d

The number of terms are: 

n = + 1

n= + 1

n=


n= 127

So there are 127 terms between 84 and 719.


Now to calculate the sum of 127 terms use the formula:

⇒ S₁₂₇= (a + l)

⇒ S₁₂₇= (85 + 715)

⇒ S₁₂₇= (800) = 50800

So the sum of the terms between 84 and 719 is 50800.