Question

A ribbon is cut into n parts. The length of each part increases such that they form a geometric progression. SPM Given the length of the fourth part of the ribbon is 9 times the length of the second part of the ribbon.

(a) Calculate the common ratio.

(b) If the total length of the ribbon is 1 476.2 m and the length of the first part is 5 cm, calculate

(i) the value of n,

(ii) the length, in cm, of the last part of the ribbon. panjang,
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Answer 1

Explanation:

`Let\ say\ r \ the \common\ ratio:\\a)a_4=r^2*a_2=9*a_2\Longrightarrow\ r=3\ (not\ -3\ since\ parts\ are\ positive)\\\\b)\\\displaystyle \sum_(i=1)^(n) a_i =a_1+a_2+a_3+...+a_n\\\\=a_1+a_1*r+a_1*r^2+a_1*r^3+...+a_1*r^(n-1)\\\\=a_1*(1+r+r^2+...+r^(n-1))\\\\=a_1*(r^n-1)/(r-1) \\\\147620=5*((3^n-1))/(3-1) \\\\3^n-1=(2*147620)/(5) \\\\3^n=59049 \\\\n*ln(3)=ln(59049)\\\\n=(ln(59049))/(ln(3)) \\\\n=10\\\\a_n=5*3^(10-1)=5*19683=98415(cm)`