Question

A small snail moving towards a point 3 cm away at a pace of 1 cm hour As if gets tired, it covers only half the distance compared hour in each succeeding hour.

Answer 1

We have,

The snail covers 1 cm. in the first hour, $\frac{1}{2}$ cm.in the next hour $\frac{1}{4}$ cm in the next hour and so on.

Then G.P.

$1,\frac{1}{2},\frac{1}{4}.......$

This G.P.

$\begin{align}

$a=1$

$d=\frac{1}{2}$

Now,

$So,$

$S_n=3$

$\Rightarrow \frac{a(1-r^n)}{1-r}=3$

$\Rightarrow \frac{1[1-{\left(\frac{1}{2}\right)}^n]}{1-\frac{1}{2}}=3$

$\Rightarrow 1-{\left(\frac{1}{2}\right)}^n=\frac{3}{2}$

$\Rightarrow {\left(\frac{1}{2}\right)}^n=-\frac{1}{2}$

Now, there is no value of n such that above equation.