SOLUTION: First question : If P=2+4+6+8+...+104 and Q=6+8+10+12+...+106 are sums of arithmetic sequence, determine which is greater, P or Q, and by how much. Second Question: Find a

Question 1151580: First question :
If P=2+4+6+8+...+104 and Q=6+8+10+12+...+106 are sums of arithmetic sequence, determine which is greater, P or Q, and by how much.
Second Question:
Find a 3 by 3 magic square using the numbers 7,8,9,14,15,16,21,22,and 23.
Third question:
Suppose there is a pile of quarters, dimes, and pennies with a total of $1.07.
a) How much of each coin can be present without being able to make change for a dollar?
b)Explain why $1.19 is the greatest amount of money it is possible to have without being able to make change for a dollar.
Fourth Question:
Find the 100th and nth term for each of the following sequences.
a. 1,5,9,13,...
b.70,120,170...
c.1,3,9....
d.8,8^4,8^7,8^10,...
e.109+7x3^32,109+8x3^32,109+9x3^32,...
Fifth question:
The first figure takes 5 matchstick squares to build, the second takes 11 to build, and the third takes 17 to build.
a) how many matchstick squares will it take to build the 8th figure?
b) how many matchstick squares will it take to build the nth figure?
c) how many matchsticks will it take to build the nth figure?
Last Question:
The first difference of a sequence is the arithmetic sequence 3,5,7,9,11,... Find the first six terms of the original sequence in each of the following cases.
a) the first term of the original sequence is 5.
b) the sum of the first two terms in the original sequence is 7.
c) the fifth term in the original sequence is 39.
THANK YOU SO MUCH FOR YOUR HELP I GREATLY APPRECIATE IT !
Answer by ikleyn(52794) (Show Source): You can put this solution on YOUR website!
.

The rule of this forum is ONE AND ONLY ONE problem/question per post.

We will be happy to help you to solve the problems, but only one per green.

----------------

In order do not leave you unhappy, I will answer only FIRST question.

If you take the difference P - Q,  you will see that almost all the terms cancel each other, 

and the only terms that survive are


    2 + 4 - 106


giving the answer  -100.


Thus P - Q = -100,  which means that  Q  is greater than  P  by  100 units.

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