Expert: Paul Klarreich - 1/5/2008

Question
The sides of the large square are 16 cm. The midpoints of the sides are joined to form a new square. Find the sum of the areas of all the squares. There are 7 squares

The interior angles of a hexagon are in an arithmetic sequence. The largest angle is 130 degrees. What are the other angles.

THe first the terms of an arithmetic series have a sum of 24 and a product of 312. What is the fourth term of the series?

These questions have really got me. Fishised every other question but I don't even know where to start with these 3.

Answer
Questioner:   Roshan
Category:  Advanced Math
Private:  No
 
Subject:  math q
Question:  The sides of the large square are 16 cm. The midpoints of the sides are joined to form a new square. Find the sum of the areas of all the squares. There are 7 squares

>> Sorry, this makes no sense.  You must have left something out.
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The interior angles of a hexagon are in an arithmetic sequence. The largest angle is 130 degrees. What are the other angles.

Let a = the smallest angle.
   d = the common difference.

Then the angles are a, a+d,...a+5d and their sum would be 6a + 15d = 720.
Also the largest,  a + 5d = 130.
Solve these two equations for a and d.
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The first the

>> three?

terms of an arithmetic series have a sum of 24 and a product of 312. What is the fourth term of the series?

Let a-d = the first term. [WEIRD, BUT IT WORKS NICELY.]
   d = the common difference.
The three terms are a - d, a, a + d.
Sum is  3a = 24, so a = 8.
Prod = a(a^2 - d^2) = 8(64 - d^2) = 312.

8(64 - d^2) = 312.

64 - d^2 = 39.

d^2 = 25,  d= 5.

Fourth term is 18.

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These questions have really got me. Fishised every other question but I don't even know where to start with these 3.