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The Rage of the Triad Chief

(10)
Posted at 9:05 pm by Miss Loi in E-Maths Questions

Continuing from the previous episode

Months later, in a tension-filled room …

This is the information they managed to extract from the Maths Tutor’s feisty aunty, before they got chased off by her reinforcement aunties via an intense attack of umbrellas, shoes, handbags etc. …

For some superstitious reason, the Maths Tutor had chosen The Temple to be located at a postal code based on a sequence with its first five terms T1, T2, T3, T4, T5 as follows:

T1 = 1 = 1
T2 = 3 = 1 + 2
T3 = 6 = 1 + 2 + 3
T4 = 10 = 1 + 2 + 3 + 4
T5 = 15 = 1 + 2 + 3 + 4 + 5

The nth term in the sequence is given by

T_n = {1/2}n(n+1)

Find T350 and hence find The Temple‘s postal code which is the solution of
5 + 10 + 15 + … + 1750.

Even though most of them failed their PSLE math, this should really, really be a simple one.

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9 Comments

  1. clarion-x's Avatar
    clarion-x says


    2010
    May
    1
    Sat
    12:13pm
     
    1

    T350= 1+2+3+4+...+349+350
    =(1+350)+(2+349)+(3+348)+...
    =351x (350/2)
    =61425

    (Sum of AP, just using non-A Level stuff to solve.)

    5+10+15+...+1750=5(1+2+3+4...+350)
    =5x61425
    =307125

  2. clarion-x's Avatar
    clarion-x says


    2010
    May
    1
    Sat
    12:15pm
     
    2

    I just realised you gave the sum of AP formula but I didn't use. D:

  3. TJK's Avatar
    TJK says


    2010
    May
    1
    Sat
    7:16pm
     
    3

    Hi Miss Loi..nice AP question

    Sorry i can't impress you with nice mathematical equations, i am simply too lazy.

    Using primary school rudimentary method:

    First time plus last term : 5 + 1750 = 1755
    Number of terms: ((1750-5) / 5) + 1 = 350
    Total sum:( 350 X 1755) / 2 = 307 125

    Using frantically pressing of P 6 calculator : 307 125

    (Or) a smart way to use TI-84 Plus: 307 125

    A level method:

    1st term: 5
    last term: 1750
    d = 2
    n = 350
    Sn = 350 /2 ( 2 (5) + ( 350 - 1)( 5) ) = 350/2 (5 + 1750)
    = 307 125

    AP is so fun =)

    Pity those people that are sabotaged by SEAB years ago by this equation
    1 + 2 + 3 + 4 + ...+ 99 + 100

  4. mathslover's Avatar
    mathslover says


    2010
    May
    2
    Sun
    11:36pm
     
    4

    "Sir, that postal code doesn't exist. Your intelligence failed." -- the henchman.



  5. 2010
    May
    5
    Wed
    12:16pm
     
    5

    Aiyo the A-Level A.P/G.P. folks (armed with super duper TI-84 Plus calculators) seem to have invaded this turf ...

    But for EMaths students without such heavy armament, Number Patterns, like its Plane Geometry counterpart in AMaths, usually requires a little 阴阳眼 prowess in order to 'see' the pattern and unravel the Da Vinci Code-styled number sequences, though there are certain standard formulae for common sequences.

    In this case there are many ways to get the simple answer, as described by clarion and TJK, but some students will have the tendency to stare at the sequence for a long, long time and wonder how on earth to 'minus every 1st-4th terms from each set of five terms' (or whatever) to obtain your 5+10+15+...+1750.

    In times like these, if you ever find yourself going deeper and deeper into a pit in the midst of your exam, it's always good to prevent a 走火入魔 situation by either

    1) revisit this part later (esp if it carries little marks) or
    2) take a deep breath, look up to the heavens, invoke the changing your point of view strategy described in your textbook OPEN your eyes, like clarion with his 阴阳眼 has done to get:

    5 + 10 + 15 + ... + 1750
    = 5(1 + 2 + 3 + ... + 350)
    = 5[(0.5)(350)(350+1)] = 307125
    Note: This is a hence question so you must use T350 to obtain the final answer.

    So sweet, so simple - even the Ah Beng's primary school-educated henchmen should have no problem with this (without the need for frantic pressing of calculators) ... such is simplicity of most Number Patterns questions, since afterall it's a Sec One topic!

  6. TJK's Avatar
    TJK says


    2010
    May
    7
    Fri
    8:24pm
     
    6

    Hi Miss Loi,

    in the end part (0.5)(350)(350 +1) also uses AP concept mah....

    now i appreciate the power of the GC (shielding power), in the past i am worried once such question approaches me like a devil.

    I still remembered the days where parents lamented SEAB for this PSLE question

    1+ 2+3+4+ ...+100

    Nice olden days

  7. X Y C's Avatar
    X Y C says


    2010
    May
    29
    Sat
    5:13pm
     
    7

    350th term: 0.5*350*(350+1)
    =61425

    Therefore, the postal code is..........

    61425*5=307125, as 1750 divided by 5 is 350. Thus, (350th term)*5=postal code!

    So smart of me!!!!

  8. AHitlerparodymaker's Avatar
    AHitlerparodymaker says


    2010
    Nov
    11
    Thu
    1:18pm
     
    8

    LOL A Hitler rant parody yay!

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    2010
    Apr
    30
    Fri
    3:07pm
     
    9

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