Posted by **Ariana** on Saturday, June 7, 2014 at 11:15am.

Find the sum of all multiples of 5 between 100 and 300 inclusive.

Ans: 8200

I do not know how to do this. Really do appreciate step by step workings and explanation.

Thanks!

- Maths! -
**Steve**, Saturday, June 7, 2014 at 12:04pm
300 = 100 + 40*5

So, set things up as an arithmetic sequence, and find that

S41 = 41/2 (100+300) = 8200

- Maths! -
**Bosnian**, Saturday, June 7, 2014 at 12:14pm
100 , 105, 110, ... 290 , 295 ,300

That is arithmetic progression.

The initial term of this arithmetic progression is a1 = 100

The common difference of successive members is d = 5

The n-th term this arithmetic progression an = 300

Use formula for n-th term of the sequence :

an = a1 + ( n - 1 ) * d

In this case :

a1 = 100

an = 300

d = 5

an = a1 + ( n - 1 ) * d

300 = 100 + ( n - 1 ) * 5 Divide both sides by 5

60 = 20 + ( n - 1 )

60 = 20 + n - 1

60 = 19 + n Subtract 19 to both sides

60 - 19 = 19 + n - 19

41 = n

n = 41

The sum of the members of a arithmetic progression is :

Sn = ( n / 2 ) * ( a1 + an ) = n * ( a1 + an ) / 2

Sn = 41 * ( 100 + 300 ) / 2

Sn = 41 * 400 / 2

Sn = 16,400 / 2

Sn = 8,200

## Answer this Question

## Related Questions

- Algebra help - f(x)=x^3-4x^2-x+4 How do I find the x-intercept for this? This is...
- Maths - When the first n positive integers are added together, their sum is ...
- Math - Algebra II - Hello, i'm currently doing functions and I was fine until I ...
- chemistry step by step for me thank a lot - What is the weight of ca(oh)2 ...
- Chemistry - When 100mL of 1.00 M Ba (NO3)2 and 100 mL of 1.00 M Na2SO4, both at ...
- Math - the sum of the integers from 1 to 10, inclusive, is 55. What is the sum ...
- Precalculus - Hello, Thanks for all of the help guys. I really appreciate it. I ...
- Algebra 2 - V=df-di/tf-ti; solve for ti Literal equations! I would really ...
- Maths - Differentiate y=(5x-2)^3(3-x)^6 using the product rule. i don't get the ...
- chemistry step by step clearly - 10L of hard water required 5.6g of lime for ...

More Related Questions