Find the sum of the multiples of 5 from 20 to 70.
Answers
Answer:
495
Step-by-step explanation:
20 + 25 + 30 + 35 + . . . . . + 70
This is an arithmetic progression
The initial term of this arithmetic progression is a1 = 20
The n-th term this arithmetic progression an = 70
The common difference of successive members is d = 5
Use formula for n-th term of the sequence :
an = a1 + ( n - 1 ) * d
In this case :
a1 = 20
an = 70
d = 5
n = ?
an = a1 + ( n - 1 ) * d
70 = 20 + (n - 1) * 5
70 - 20 = 5n -5
50 = 5n - 5
50 + 5 = 5n
55 = 5n
55 = n
5
11 = n
n = 11
The sum of the members of a arithmetic progression is :
Sn = ( n / 2 ) * ( a1 + an )
= 11 / 2 * ( 20 + 70 )
= 11 / 2 * ( 90 )
= 990 / 2
Sn = 495
HOPE YOU UNDERSTOOD
THANK YOU
Given:
Multiples of 5 from 20 to 70
To find:
Sum of the multiples of 5 from 20 to 70 = ?
Calculation:
This sum can be solved in two step.
Step 1 of 2
Write the multiples of 5 from 20 to 70.
They are 25, 30, 35, 40, 45, 50, 55, 60, and 65
Step 2 of 2
Add all the multiples of 5 from 20 to 70
25 + 30 + 35 + 40 + 45 + 50 + 55 + 60 + 65 = 475
Final answer:
The sum of the multiples of 5 from 20 to 70 is 475.