Question

A leprechaun places a magic penny under a​ girl's pillow. The next night there are 2 magic pennies under her pillow. Each night the number of magic pennies doubles. How much money will the girl have after 19 ​nights

Answer 1

Answer:

524288

Step-by-step explanation:

No of nights is 19

No of coins each night n^2

So it is 2^19

Answer 2

The number of money will the girl have after 19 ​nights is $2^{19}$.

Step-by-step explanation:

The given sequence are:

2, 4, 8, 16, .... up to 19th terms

The above sequence are in GP.

Here, first term(a) = 2, common ratio(r) = 2 and n = 19

∴ The number of money will the girl have after 19 ​nights = ?

To find, how much money will the girl have after 19 ​nights =?

We know that,

$a_{r} =ar^{n-1}$

⇒ $a_{19} =(2)2^{19-1}$

⇒$a_{19} =(2)2^{18}=2^{18+1} =2^{19}$

Hence, the number of money will the girl have after 19 ​nights is $2^{19}$.