Question 696834

A tortoise travelled 4096 m in week one. Each week, it travelled half as far as the previous week. In what week will the tortoise travel 4 m? Please show me using a formula or equation. I know the answer because I used the calculator but I still want to know how to find the answer using a formula or equation.I'm in grade 7 can you explain, because the previous time i didnt understand. Help!


The terms represent a geometric sequence with the first term, or {{{a[1]}}}: 4,096, r, or common ratio: {{{1/2}}}, and n: the week-number that the tortoise will travel 4 m


Geometric sequence: {{{a[n] = a[1]r^(n - 1)}}}


Therefore, {{{a[n] = a[1]r^(n - 1)}}} becomes: {{{a[n] = 4096(1/2)^(n - 1)}}}


{{{4 = 4096(1/2)^(n - 1)}}} 


{{{4/4096 = (1/2)^(n - 1)}}}


{{{1/1024 = (1/2)^(n - 1)}}}

 
{{{log (1/2, (1/1024)) = n - 1}}}


{{{log (1/1024)/log(1/2) = n - 1}}}


{{{log (1/1024)/log(1/2) = 10}}}, so:


10 = n - 1


n = 10 + 1


The tortoise will travel 4 m in week n, or week {{{highlight_green(11)}}}


You can USE MS Excel to check!!


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