# Thread: Arithmetics question, so confused :(

1. ## Arithmetics question, so confused :(

Hi guys & Girls Ive come across this question in my assignment for math, surely i dont have enough information to get an answer?

The Sum of the first 10 terms of an arithmetic series is 165 and the sum of the next 10 terms is 445. Find the sum of the terms 21-30.

SUM = n/2 [2a (n-1)]d

n= number of terms (10 for each formula as only 10 terms are added together i.e. 1->10 = 10 and 11->20 = 10???)

a = First Term in series (None given)

d = Common difference (also not given)

445 = 20/2 [2a (20-1)]d
165 = 10/2 [2a (10-1)]d

can't use linear equation there because a for the 445 will be different from a for 165, and d isnt known

all the other formulae i have come across either require d or at least a couple of values in the sequence so I can work out d

pfft, surely it's impossible?

2. You're on a right track.

First 10
a + (a+d) + (a+2d) + ...+ (a+9d) = 165 = 10a + 45d = 165

Second 10
(a+10d) + (a+11d) + (a+12d) + ...+ (a+19d) = 445 =
(a+10d) + (a+10d+d) + (a+10d+2d) + ...+ (a+10d+9d) = 10a + 45d + 100d =
10a + 145d = 445

Now you can solve for a and d if you wish, but you may wish to hold off on that.

Third 10 - You should be able simply to write this one down.
10a + 245d = ??

Of course, there is always the really easy way. This is all linear. Why mess with it?

445 - 165 = 280

?? - 465 = 280

3. thanks mate youve been a lot of help, cudnt get that one round ma head