ARCH-MM-04: Sigma Notation (Fence-Post n-m+1 Terms) & Periodic Recurrence Relations (u_{n+1} = f(u_n))

Full 15-Q Timed Drill

Step 1 of 6 • The Core Idea

ARCH-MM-04: Why the 155s Classroom Method Fails Under the 90s Clock

Standard Classroom Method (Too Slow)~155s (Blows 90s Clock)

Splitting into

a\left(\sum_{r=1}^{24} r - \sum_{r=1}^{4} r\right) + b(24 - 5 + 1)

requires evaluating

\frac{1}{2}(24)(25)

and

\frac{1}{2}(4)(5)

separately, taking ~135s.

The Fast ShortcutTarget: 45s (Saves 110s)

Line 1 (Fence-Post Count): Number of terms is

N = 24 - 5 + 1 = 20

; first term

u_{5} = 13

, last term

u_{24} = 51

.
**Line 2 (Average

\times

Count):**

\frac{20}{2}(13 + 51) = 640

(30s).

Where Students Lose Time: In 9 past UAT-UK questions (2.2% of Mathematics 2), candidates lose 110s by classic fence-post off-by-one error when lower summation index m > 1. Instead, apply MM2 with Maths 1 skill M2.6.

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