A sequence is defined such that, for all values n3 , an=(an1) 2(an

Question

A sequence is defined such that, for all values  n>3, a_{n}=(a_{n−1})^{2}−(a_{n−2})^{2}.  If  a_{1}=1, a_{2}=2 , and  a_{3}=3 , what are the values of  a_{5}  and  a_{7}

yashikaaggarwal · Answer

A4 = (A3)^2-(A2)^2
A4 = (3)^2-(2)^2
A4 = 9-4
A4 = 5

A5 = (A4)^2-(A3)^2
A5 = (5)^2-(3)^2
A5 = 25-9
A5 = 16

A6 = (A5)^2-(A4)^2
A6 = (16)^2-(5)^2
A6 = 256-25
A6 = 231

A7 = (A6)^2-(A5)^2
A7 = (231)^2-(16)^2
A7 = 53361-256
A7 = 53105

A5 = 16
A7 = 53105

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Archit3110 · Answer

using the given relation 
m]n>3, a_{n}=(a_{n−1})^{2}−(a_{n−2})^{2}.  If  a_{1}=1, a_{2}=2 , and  a_{3}=3 ,
we can find values of a4 which would be 
(a3)^2-(a2)^2 ; 5
similarly a5,a6 & a7 can be determined
which would be
a5=16
a6=231 and 
a7= 53105

agrasan · Answer

A6 is 231 when we solve the equation
A5 is 16
However, we don't need to solve an entire equation to arrive at a7 as (231)^2 will have 1 at the unit digit, and subtracting (16)^2 which is 256 will give 5 at the unit digit for a7, and we have only one option that matches this. This will save time.

A sequence is defined such that, for all values n>3 , an=(an1) 2(an

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\(a_{5}\)	\(a_{7}\)
		4
		5
		16
		25
		52664
		53105

\(a_{5}\)	\(a_{7}\)
		4
		5
		16
		25
		52664
		53105

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