A tree, in each year grows 5 cm less than it grew in the previous year. If it grew half a metre in the first year, then the height of the tree (in metres ) when it ceases to grow, is

Let $a_{n}$ denote the growth of height in the $n^{t h}$ year. We have

$a_{1} = 50 cm, a_{r} = 50 - 5 (r - 1) = 55 - 5 r$

The tree ceases to grow in the $r^{t h}$ year where $a_{r} = 0 \Rightarrow r = 11$

So height of tree is

$\begin{array}{l} a_{1} + a_{2} + \dots + a_{10} \\ = \frac{10}{2} [50 + 5] cm = 275 cm = 2.75 m \end{array}$

Related content