Find the sum of all multiples of 7 between 400 and 500.

Question

kainui · Answer

Any ideas?

anonymous · Answer

Well, I'm stuck myself and that is all the information that was provided. 
Other than that, the answer at the back of the book is 6,321.

anonymous · Answer

do you know the formula?

kainui · Answer

There is no need to have formulas for this.

anonymous · Answer

the its hard

kainui · Answer

Well you can use a formula, but you won't learn anything other than how to replace letters with numbers.

anonymous · Answer

the equation should be |dw:1404106122330:dw|

anonymous · Answer

Sn = n÷2 (a+l)
or 
Sn = n÷2 {2a+(n-1)d}

anonymous · Answer

Those two are the equations. I used both but I'm pretty sure I made some sort of a mistake

anonymous · Answer

well then what would have been your first step??

hartnn · Answer

which will be the very first number, after 400, which is a multiple of 7 ? can you find that ?

anonymous · Answer

406

hartnn · Answer

right, and which will be the last number? just before 500, which is divisible by 7 ?

anonymous · Answer

it's 497

hartnn · Answer

correct,
so we have our series from

406,413,420,... ..497
right ?
can you tell, how may terms will be there in all ?

anonymous · Answer

58 × 7 = 406 
71 × 7 = 497 
then find the mean.
(406 + 497)/2 = 451.5
well there is 17 terms in this sequence so
451.5 * 17 = 6321

hartnn · Answer

he/she used the formula :
$\Large S_n = (n/2) [a_1 +a_n]$

hartnn · Answer

which is sum for n terms in an arithmetic series

anonymous · Answer

Oh! I got it :O

hartnn · Answer

glad to hear that :)
$\Huge \mathcal{\text{Welcome To OpenStudy}\ddot\smile} $

anonymous · Answer

But, how do I find out how many terms there are? 
Oh no. -.- That was a dumb question. Got it.

hartnn · Answer

i get 14 terms, how did u get 17 terms ?

anonymous · Answer

no your right 14 i messed up on my paper i got mixed up

hartnn · Answer

It was a good question, i find it like this : 
range = 500-400 = 100
100/7 = 14 (rounded)

alternate way :

497 is the n'th term, common difference = 7 , a1 = 1st term =406 

497 = 406 + 7(n-1)
n=14

hartnn · Answer

i used the n'th term formula there
$a_n = a_1 +(n-1)d$

anonymous · Answer

Thanks both of you :)

hartnn · Answer

welcome ^_^

goformit100 · Answer

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