# arithmetic sequences

• May 24th 2009, 04:52 AM
Tweety
arithmetic sequences
A polygon has 10 sides. The lengths of the sides, starting with the smallest, form an arithmetic series. The perimeter of the polygon is 675 cm and the length of the longest side is twice that of the shortest side. Find, for this series:

(a) The common difference.

(b) The first term.
• May 24th 2009, 05:55 AM
Jester
Quote:

Originally Posted by Tweety
A polygon has 10 sides. The lengths of the sides, starting with the smallest, form an arithmetic series. The perimeter of the polygon is 675 cm and the length of the longest side is twice that of the shortest side. Find, for this series:

(a) The common difference.

(b) The first term.

Let \$\displaystyle a\$ be the shortest side and \$\displaystyle d\$ the difference so the sides are

\$\displaystyle a, a+d, a+2d,\; \cdots \; a + 9d\$

Adding gives \$\displaystyle 10a + 45d = 675\, (*)\$, the condition that the longest is twice the shortes gives \$\displaystyle 2a = a + 9d\$ or \$\displaystyle a = 9d\$. Use this in (*).