A carpenter is cutting wooden planks for a staircase

MATHEMATICS · Multi-part · A Level · Mathematics · Sequences and series · Sequences and series

Problem

A carpenter is cutting wooden planks for a staircase. The length of the first plank is

200\,\text{cm}

, and each successive plank is

3.5\,\text{cm}

shorter than the previous one. (i) Write the lengths of the first five planks. (ii) Obtain an expression for the length of the

n

th plank. (iii) Determine the greatest value of

n

for which the plank length is still greater than

150\,\text{cm}