Question

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.

Answer 1

574^2/2
=164738 I think

Answer 2

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

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:

`S_n=(n)/(2)(2a+(n-1)d)`

`S_(574)=(574)/(2)(2* 1+(574-1)* 1)`

`S_(574)=165,025`

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