Need help on an arithmetic series. Please help.

Right basically i have a question from my homework which i have no idea how to approach, i was wondering if you could explain to me. Theres a rep for the one who helps most. Heres the question:

A polygon has 10 sides. The lengths of the sides, starting with the smallest, form an arithmetic series. The perimeter of the polygon is 675cmm and the length of the longest side is twice that of the shortest side. Find a)the common difference and b)the first term.

Please help i have no idea how to create the series or work out the figures, but i guess the formula Sn=n/2(2a+(n-1)d) probably comes in use. :biggrin:

Reply 1

Chewwy

Sn = 675
l = 2a
n = 10

Sn = 675 = 10(2a+a)/2 = 15a
a = 45

675 = (10/2)(2(45) + (10-1)d)
135 = 90 + 9d
d = 5

Reply 2

Gaz031

I'll give you an idea of how to do it but I'm sure you'll enjoy the problem more if I don't give you the entire answer.
Let 'a' be the length of the shortest side and let the common difference be d.
Then the nth side has length a+(n-1)d.
The perimeter is the sum of the lengths of the 10 sides - write this down in terms of a and b, then equate it to the value given to form an equation with two unknowns.
From the formula we have for the length of the nth side you can find the length of the shortest and longest side in terms of a and d, equate these two expressions to form another equation in two unknowns.
Solve these two equations simultaneously.