SOLUTION: `Solve the following problems completely and logically. Problem 1: Construct a difference table to determine the next term in the sequence 17,15,25,53,105,18, ___. Problem 2:

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Question 1158294: `Solve the following problems completely and logically.
Problem 1: Construct a difference table to determine the next term in the sequence
17,15,25,53,105,18, ___.
Problem 2: Determine the nth-term formula for the number of square tiles
in the nth figure. Then use this to find the number of square tiles
in the 30th figure.
a1=2squares, a2=4squares, a3=6squares, a4=8squares, a5=10squares
Problem 3: One straight cut across a pizza produces 2 pieces. Two cuts can produce a
maximum of 4 pieces. Three cuts can produce a maximum of 7 pieces. Four cuts can produce
a maximum of 11 pieces. Find the maximum number of pieces that can be produced''.
I hope you receive the copy of the problem via reply on the mail... PLEASE HELP ME WITH MY MATH SUBJECT!!!
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!



Problem 1....

I will ignore the last number in the sequence you show, since it is almost certainly a typo.

(By the way, it would be polite of you to make sure the problem is correct before you post it....)

So I will use the first five of the terms you show and use those to find the correct 6th term and the new 7th term.
     17    15    25    53    105
        -2    10    28    52
           12    18    24
               6     6

The row of third differences is constant. To find two more terms in the sequence, add two more 6's in that row and work back up the array.
     17    15    25    53    105    187   305
        -2    10    28    52     82    118
           12    18    24     30    36
               6     6     6     6


we find the 3rd differences to be all equal to
so, the next 2nd difference will be
the next 1st difference will be
thus, the next term will be


Problem 2....

; ; ; ; ...

Clearly the nth term is ; then


Problem 3....

(Note your statement of the problem is not complete....)

The numbers of regions for 1, 2, 3, and 4 cuts are

2, 4, 7, 11

Compare this sequence to the sequence of triangular numbers:

1, 3, 6, 10

The numbers in this sequence are each 1 more than the corresponding triangular number.

The formula for the n-th triangular number is

The formula for the maximum number of pieces of pizza with n cuts is



Answer by MathTherapy(10553)   (Show Source): You can put this solution on YOUR website!
`Solve the following problems completely and logically.
Problem 1: Construct a difference table to determine the next term in the sequence
17,15,25,53,105,18, ___.
Problem 2: Determine the nth-term formula for the number of square tiles
in the nth figure. Then use this to find the number of square tiles
in the 30th figure.
a1=2squares, a2=4squares, a3=6squares, a4=8squares, a5=10squares
Problem 3: One straight cut across a pizza produces 2 pieces. Two cuts can produce a
maximum of 4 pieces. Three cuts can produce a maximum of 7 pieces. Four cuts can produce
a maximum of 11 pieces. Find the maximum number of pieces that can be produced''.
I hope you receive the copy of the problem via reply on the mail... PLEASE HELP ME WITH MY MATH SUBJECT!!!
Why does this woman continue to PLAGIARIZE other people's work? Since she always does it, why can't she refer to the source, 
and let the person who asked for help know that the solution(s) she provided was someone else's?

This problem is EXACTLY the same as: 
Question 1157621: Solve the following problems completely and logically.
Problem 1: Construct a difference table to determine the next term in the sequence
17,15,25,53,105,18, ___.
Problem 2: Determine the nth-term formula for the number of square tiles
in the nth figure. Then use this to find the number of square tiles
in the 30th figure.
a1=2squares, a2=4squares, a3=6squares, a4=8squares, a5=10squares
Problem 3: One straight cut across a pizza produces 2 pieces. Two cuts can produce a
maximum of 4 pieces. Three cuts can produce a maximum of 7 pieces. Four cuts can produce
a maximum of 11 pieces. Find the maximum number of pieces that can be produced
(Scroll Down for Answer!)
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