Respuesta :
Answer: The answer is yes.
Step-by-step explanation: Given that Julie's brother owe $40 to her. He says instead of paying her this amount, he will give her $2 taday and double the amount she has each day for 6 days. We are to check whether Julie should accept the offer or not.
Now,
On 1st day, amount paid by Julie's brother = $2,
On 2nd day, amount paid by Julie's brother = $4,
On 3rd day, amount paid by Julie's brother = $8,
On 4th day, amount paid by Julie's brother = $16,
On 5th day, amount paid by Julie's brother = $32,
On 6th day, amount paid by Julie's brother = $64,
On 7th day, amount paid by Julie's brother = $128.
Therefore, these amounts will form a geometric sequence, where the first term, 'a' is 2 and the common ration, 'r' is 2. Number of terms is 7.
So, the total sum paid by Julie's brother in seven days is given by
[tex]S=2+4+8+16+32+64+128\\\\\Rightarrow S=\dfrac{2(2^7-1)}{2-1}=\dfrac{2\times 127}{1}=254>40.[/tex]
Hence, Julie should accept the offer.
