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a) After being involved in an accident a year ago, Salim

Berikut ini adalah pertanyaan dari yana33168 pada mata pelajaran Matematika untuk jenjang Sekolah Menengah Atas

A)After being involved in an accident a year ago, Salim joined a jogging program. For the first week, the program trainer suggested him to jog slowly for 12 minutes each day. Then for each of the subsequent weeks, Salim has to increase the time by 6 minutes for his jogging.
(i) Which week will Salim jog for 30 minutes?

Jawaban dan Penjelasan

Berikut ini adalah pilihan jawaban terbaik dari pertanyaan diatas.

Jawab:

Salim will jog for 30 minutes on the 4th week.

Penjelasan dengan langkah-langkah:

1st week: 12 minutes

2nd week and on: + 6 minutes / week

Because the difference is constant (6 minutes), the number of minutes create an arithmetic sequence. Without using the arithmetic sequence formula, we can find:

\large\text{$\begin{array}{|r|c|c|c|c|}\cline{1-5}\rm Week & 1 & 2 & 3 & 4\\\cline{1-5}\rm Minutes & \bf 12 & \bf18 & \bf24 & \bf30\\\cline{1-5}\end{array}$}

So, Salim will jog for 30 minutes on the 4th week.

Another Way (Using Formula)

The formula of arithmetic sequence is as follows:

\Large\text{$\displaystyle\boxed{a_n=a_1+(n-1)d}$}

It's already known that:

  • aₙ = 30
  • a₁ = 12
  • d = 6

So, by occupying the formula and substituting the value of aₙ , a₁ and d:

\text{$30=12+(n-1)6$}\\\text{$30=12+6n-6$}\\\text{$30=6n+12-6\qquad\dots$(\sf arrange the right side)}\\\text{$30=6n+6$}\\\text{$24=6n\qquad\qquad\qquad\dots$(\sf substract both sides by 6)}\\\bf n = 4

So, Salim will jog for 30 minutes on the 4th week.

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Last Update: Mon, 31 Jan 22
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