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MathRevolution
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0akshay0
\(a_n\) = \(a_{n-1}\) + \(a_{n-2}\) ....+ \(a_1\) ----------------------1

\(a_{n+1}\) = \(a_{n}\) + \(a_{n-1}\) ....+ \(a_1\) =\(a_{n}\) + \(a_{n}\) ----------------------2

\(a_{n+2}\) = \(a_{n+1}\) + \(a_{n}\)+ \(a_{n-1}\) + .... + \(a_1\) ----------------------3

\(a_{n+2}\) = \(a_{n}\) + \(a_{n}\) + \(a_{n}\) + \(a_{n}\) = 4\(a_{n}\) = 4p ( by using st. 1,2 and 3 )


Question is asking what is \(a_{n+2}\)
Given \(a_n\) = \(a_{n-1}\) + \(a_{n-2}\)+\(a_{n-3}\)...........+ \(a_1\) = p

\(a_{n+1}\) = \(a_n\) + \(a_{n-1}\) + \(a_{n-2}\)+\(a_{n-3}\)........... + \(a_1\)
= p + p = 2p

\(a_{n+2}\) = \(a_{n+1}\) + \(a_n\) + \(a_{n-1}\) + \(a_{n-2}\)+\(a_{n-3}\)........... + \(a_1\)
= 2p + p + p = 4p

Answer is B
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0akshay0
\(a_n\) = \(a_{n-1}\) + \(a_{n-2}\) ....+ \(a_1\) ----------------------1

\(a_{n+1}\) = \(a_{n}\) + \(a_{n-1}\) ....+ \(a_1\) =\(a_{n}\) + \(a_{n}\) ----------------------2

\(a_{n+2}\) = \(a_{n+1}\) + \(a_{n}\)+ \(a_{n-1}\) + .... + \(a_1\) ----------------------3

\(a_{n+2}\) = \(a_{n}\) + \(a_{n}\) + \(a_{n}\) + \(a_{n}\) = 4\(a_{n}\) = 4p ( by using st. 1,2 and 3 )


Question is asking what is \(a_{n+2}\)
Given \(a_n\) = \(a_{n-1}\) + \(a_{n-2}\)+\(a_{n-3}\)...........+ \(a_1\) = p

\(a_{n+1}\) = \(a_n\) + \(a_{n-1}\) + \(a_{n-2}\)+\(a_{n-3}\)........... + \(a_1\)
= p + p = 2p

\(a_{n+2}\) = \(a_{n+1}\) + \(a_n\) + \(a_{n-1}\) + \(a_{n-2}\)+\(a_{n-3}\)........... + \(a_1\)
= 2p + p + p = 4p

Answer is B


I did the same thing.
St. 1,2 and 3 explains how \(a_{n+2}\) = 4\(a_n\) :)
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==> Since an =an-1+an-2+an-3+….+a2+a1 =p,
an+1 =an+ an-1+an-2+an-3+….+a2+a1=p+p=2p
an+2=an+1+an+an-1+an-2+an-3+….+a2+a1=2p+p+p=4p.

Hence, the answer is B.
Answer: B
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Hello everyone!

Could anyone know where can I find more exercises like this one?

It has been really difficult for me when I have to decipher the terms represented with letters.

Thank you so much in advance!
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jfranciscocuencag
Hello everyone!

Could anyone know where can I find more exercises like this one?

It has been really difficult for me when I have to decipher the terms represented with letters.

Thank you so much in advance!

Hey jfranciscocuencag,

You can filter out for the type sequences in the link below.

https://gmatclub.com/forum/search.php?v ... s&style=11

Hope it helps.

Posted from my mobile device
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Afc0892
jfranciscocuencag
Hello everyone!

Could anyone know where can I find more exercises like this one?

It has been really difficult for me when I have to decipher the terms represented with letters.

Thank you so much in advance!

Hey jfranciscocuencag,

You can filter out for the type sequences in the link below.

https://gmatclub.com/forum/search.php?v ... s&style=11

Hope it helps.

Posted from my mobile device

Thank you Afc0892 !
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0akshay0
\(a_n\) = \(a_{n-1}\) + \(a_{n-2}\) ....+ \(a_1\) ----------------------1

\(a_{n+1}\) = \(a_{n}\) + \(a_{n-1}\) ....+ \(a_1\) =\(a_{n}\) + \(a_{n}\) ----------------------2

\(a_{n+2}\) = \(a_{n+1}\) + \(a_{n}\)+ \(a_{n-1}\) + .... + \(a_1\) ----------------------3

\(a_{n+2}\) = \(a_{n}\) + \(a_{n}\) + \(a_{n}\) + \(a_{n}\) = 4\(a_{n}\) = 4p ( by using st. 1,2 and 3 )

Hence option B.

Thank you, nice solution!
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