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Pt1420 Unit 6 Lab Report

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Row 1
1
1x22
1(odd)
Row 2
1+2
2x32
3 (odd)
Row 3
1+2+3
3x42
6 (even)
Row 4
1+2+3+4
4x52
10 (even)
Row 5
1+2+3+4+5
10x112
15 (odd)
Row n
1+2…+n
n(n+1)2 n/a

A pattern I noticed when filling in the table was how the answer to the 2nd column increase in order. (The difference between each answer is - 1,2,3,4,5). I can predict last column is always going to be equal to the 2nd column. Another prediction I could explore how the last column has 2 even and 2 odd numbers.

Row 6: 1+2+3+4+5+6 = 6x7 ÷ 2 = 21 (odd)
Row 7: 1+2+3+4+5+6+7 = 7x8 ÷ 2 = 28 (even)
Row 8: 1+2+3+4+5+6+7+8 = 8x9 ÷ 2 = 36 (even)

This shows how the 2 odd & 2 even method continues throughout the sequence, this would be correct as the numbers from the last column (1,3,6,10,15,21,28,36…) …show more content…
The y values multiply by 2 each time proving that the sequence is geometric. By using an example it helps me to clarify how my sequence doesn’t follow the geometric pattern.

https://www.google.es/search?q=exponential+growth+sequence&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiPro-CnaDXAhVDVBQKHeDbD-wQ_AUICigB&biw=1344&bih=781#imgrc=qhfPt-JWfAH69M:

Using Mathematical Symbols:

Row 1
1
1x22
1
Row 2
2
∑n
1
2x32
3
Row 3
3
∑n
1
3x42
6
Row 4
Etc ….
4x52
10
Row 10 ..
10
∑n
1
10x112
55
Row n .. n ∑n n=1 n² + n2 n The sigma notation is used to show that you start at the first value and finishes at the value at the top (in this case 2). By using the sigma notation it shows more mathematical understanding/technique instead of writing 1+2+3+4 ….

I decide to see if the sn formula (geometric) sn = u1(rn-1)r-1applied to this sequence:

u2=3 u5=15 sn = u1 (rn-1)r-1

I can see that my sequence (1,3,6,10,15) is not a geometric sequence as it isn’t multiplied by the same number each time & is unable to fit into the formula.

Totals of 1x2 ÷ 2 Column

n
1
2
3
4
5
sequence
1
3
6
10
15
difference
2
3
4
5
...
2nd difference
1
1
1
1
...

2nd Difference is the same 1 meaning it’s quadratic!
2nd Difference ÷ 2 =

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