Question

Please find attached.

Answer 1

do you know what makes an "arithmetic sequence"?

Answer 2

it means each term is a constant more than the previous one.
for example
x, x+k, x+2k is an arithmetic sequence.

Answer 3

one way to solve this is say the 3 terms are
x-k, x, x+k
they add to 30:
x-k+x+x+k= 30
3x= 30
x=10

their product is 640:
(x-k)*x*(x+k)= 650

sub in x=10 into this equation and find k. then you can find x-k, x and x+k
as the 3 terms.

Answer 4

I thought I arithmetic sequence was a+(a+d)+(a+2d)???

Answer 5

it is, but of course you could go back from the (if we started in the middle):
(a-d), a, (a+d), (a+2d) ...

but if we use (a-d), a, (a+d), it makes the first equation very easy to solve. It is a trick, but a useful one. otherwise we have to solove
3a+3d= 30
a+d= 10

and then use that in a(a+d)(a+2d)= 640
which looks complicated

Answer 6

could you solve using systems?

Answer 7

well, we could do this
a+ (a+d) + (a+2d)= 30
3a+3d= 30
(a+d)= 10

their product:
a(a+d)(a+2d)
replace a+d with 10 (see above)
a(10)(10+d) (notice that a+2d = a+d + d = 10+d)
so
a(10)(10+d) = 640
a(10+d)= 64


so we have
a+d=10 and a(10+d)= 64
we can solve these for a and d. Can you finish?

Answer 8

yes

Answer 9

thanks

Answer 10

but the other way is nice. It uses symmetry (a-d), a, (a+d)