O lvl E Maths: Number Patterns

RGS P1 Prelim 1997 Q20 (Simple question)

(i) Complete the number pattern
1 = 1
1 + 2 + 1 = 4
1 + 2 + 3 + 2 + 1 =
1 + 2 + 3 + 4 + 3 + 2 + 1 =
1 + 2 + 3 + 4 + 5 + 4 + 3 + 2 + 1 =

(ii) What sort of numbers do you get?

(iii) Find 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

(iv) How is your answer connected to the middle number?

(v) Write down the answer for 1 + 2 + 3..... 49 + 50 + 49 .... 3 + 2 + 1

(vi) If 1 + 2 + 3+ .... (k - 1) + k + (k - 1) ..... 3 + 2 + 1 = 196, find the value of k.

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Answer:

(i)
1 = 1
1 + 2 + 1 = 4
1 + 2 + 3 + 2 + 1 = 9
1 + 2 + 3 + 4 + 3 + 2 + 1 = 16
1 + 2 + 3 + 4 + 5 + 4 + 3 + 2 + 1 = 25

(ii) Squares
i.e. 1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25

(iii) 64

(iv) The answer is the square of the middle number, i.e. 8²

(v) 50² = 2500

(vi) k² = 196
Hence, k = 14

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