Question 0411

Arithmetic and Geometric Progressions (APs, GPs)

2011 Paper 1 Question 9 Variant

Question

(i)

A company is digging a tunnel. Using machine

{A,}

the distance dug on the first day is

{274}

metres. On each subsequent day, the distance dug is

{9}

metres less than on the previous day. Digging continues daily up to and including the day when a distance of less than

{5}

metres is dug. What is the distance dug on the

{9\textrm{th}}

day, and what is the total distance dug when drilling is completed?

[6]

(ii)

Using machine

{B,}

the distance dug on the first day is also

{274}

metres. On each subsequent day, the distance dug is

{\frac{1}{4}}

of the distance dug on the previous day. How many days does it take for the distance dug to exceed

{95\%}

of the theoretical maximum distance?

[4]