The imaginary monster Dracula is 574 years old, according to legend. Since that very first birthday long ago, when he happily blew out 1 candle on a cake decorated with drippy red frosting, how many birthday candles has he blown out in his whole horrifying life? Assume that Drac has always blown out exactly n candles on his nth birthday.

Respuesta :

574^2/2
=164738 I think

Answer:

165,025 birthday candles has been blown out by the Dracula in his whole horrifying life.

Step-by-step explanation:

Present age of the monster Dracula = 574 years

Number of candles on his first birthday = 1

Number of candles on his second birthday = 2

Number of candles on his third birthday = 3

Number of candles on nth birthday= n

The sequence coming out be is an arithmetic sequiece:

1,2,3,4......

a = 1, d = 1

if n = 574

Then sum of the nth term is given as:

[tex]S_n=\frac{n}{2}(2a+(n-1)d)[/tex]

[tex]S_{574}=\frac{574}{2}(2\times 1+(574-1)\times 1)[/tex]

[tex]S_{574}=165,025[/tex]

165,025 birthday candles has been blown out by the Dracula in his whole horrifying life.