Find the sum of the positive multiples of 5 up to 500
Answers
Answer:
Answer: multiples are 105, 110, 115, 120 ,125,130,135,140,145,150,155,160,165,170,175,180,185,190 and 195 and their sum is 2850.
Step-by-step explanation:
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Given : positive multiples of 5 up to 500
To Find : Sum
Solution:
Arithmetic sequence : Sequence of terms in which difference between one term and the next is a constant.
This is also called Arithmetic Progression AP
Arithmetic sequence can be represented in the form :
a, a + d , a + 2d , …………………………, a + (n-1)d
a = First term
d = common difference = aₙ-aₙ₋₁
nth term = aₙ = a + (n-1)d
Sum of Arithmetic sequence (AP) is called Arithmetic series
Sₙ = (n/2)(2a + (n - 1)d) or (n/2)( first + nth Term)
positive multiples of 5 up to 500
5 , 10 , 15 , ... , 495 , 500
a = 5
d = 5
500 = 5 + (n - 1)5
=> 100 = 1 + n - 1
=> n = 100
Hence 100 terms
So Sum = (100/2)(5 + 500)
= 50 * 505
= 25250
Hence, the sum of the positive multiples of 5 up to 500 is 25250
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