Number Sequences
Explicit • Recursive • Sum of all terms • Geometric Series
Test Your Knowledge
Centered Polygons
General Sequences
Geometric Series
Shape:
Centered Square
Centered Hexagon
Centered Triangle
Centered Octagon
Year n:
4
n=4
Year
4
Points:
25
| Sum:
41
Sequence (use ? for gaps):
Analyze
📏 5,8,11,14,17 (linear)
📐 2,9,22,41,66 (quadratisch)
📐 3,10,21,?,55
📐 1,4,10,?,31
n =
a
n
S
n
Difference Table
a
1
=
q =
n =
Berechnen
🌟 M10
a₁=1, q=2.5, n=6, m=6.6, Δm=13,4
🌟 Omega Centauri
a₁=1, q=2.72, n=6, m=3.9, Δm=16.6
S
n
= ?
a
n
= ?
Terme und Partialsummen
a
k
Partialsumme S
k
Vergleich M10 (q=2.5) vs. Omega Cen (q=2.72) – Terme a
k
von k=10 bis 16
M10 (q=2.5)
Omega Centauri (q=2.72)
Die Differenz wächst ab k≈12 stark an – exakter Ausdruck der unterschiedlichen Sternpopulationen.
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