Answer:
£11, £33, £22
Step-by-step explanation:
F:D:S= 1:3:2
Fiona £11
Dan £33
Stephen £22
If

is odd, then

while if

is even, then the sum would be

The latter case is easier to solve:

which means

.
In the odd case, instead of considering the above equation we can consider the partial sums. If

is odd, then the sum of the even integers between 1 and

would be

Now consider the partial sum up to the second-to-last term,

Subtracting this from the previous partial sum, we have

We're given that the sums must add to

, which means


But taking the differences now yields

and there is only one

for which

; namely,

. However, the sum of the even integers between 1 and 5 is

, whereas

. So there are no solutions to this over the odd integers.
Step-by-step explanation:
The sum of the interior angles of a convex regular polygon is 180 times (n-2), where n is the number of sides. Since we already know the sum, we can write 3,960 = 180(n-2). If you solve for n in this equation, you will have the number of sides.
Answer:
No
Step-by-step explanation:
n₁=4
n₂=9
n₃=16
We can see that all three numbers are perfect squares of one higher than the figure number
So, n₁₅=(15+1)²=16₂=256
256≠225
There's not enough info to know the exact number for each. There would be at least a 2 different answers because either could be calculated to conclude the end result.