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Algebra

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If p(n+1)+p(n-1)=p(n) for every natural number ‘n’then for what values of natural number  ‘a’ will p(n+a)=-p(n)

a)3   b)2   c)4    d)6

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p(n+1)+p(n-1)=p(n)(eq 1)

taking n as n+1

p(n+2)+p(n)=p(n+1)(eq 2)

taking n as n+2 in eq 1

p(n+3)+p(n+1)=p(n+2)

substituting p(n+2) from equation 2 we will get

P(n+3)=p(n+1)-p(n)-p(n+1)

so p(n+3)=-p(n)

 

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