Question

Answer all questions.

Jawab semua soalan.
Given an arithmetic progression with first term 36 and common difference - 4 . Find
the number of tennis in the progression if the sum of all terins is 0.
Diberi suatu janjang arimetik dengan sebutan pertama 36 dan beza sepunya - 4.
Cari bilangan sebutan janjang itu jika hasil tambah bagi semua sebutannya ialah 0.
[2 marks]
[2 markah]​

Answer 1

18

Explanation:

The first four terms of your sequence are

a₁ = 34

a₂ = 30

a₃ = 26

a₄ = 22

If the sum of all the terms is zero, there must be a set of negative terms corresponding to the positive ones.

That is, the last four terms must be -22, -26, -30, -34.

So, one strategy is to find the number of positive terms and multiply by 2.

Each term (aₙ) in your sequence is 4 units less than the preceding term (aₙ₋₁) .

The explicit formula is

aₙ= 34 - 4(n - 1)

Assume aₙ = 0. Then

`\begin{array}{rcl}0 & = & 34 - 4(n-1)\\& = & 34 - 4n + 4\\& = & 38 - 4n\\4n & = & 38\\n & = & 9.5\\\end{array}`

We can't have a fractional number of terms, so

n = 9 (that is, the last positive number is 2).

There must be a corresponding sequence of nine negative numbers.

Your complete sequence has 18 terms.