A sequence is defined by the recursive function #f(n+1) = f(n) - 2 #. If # f(1) = 10# , what is # f(3 #)?

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Oct 11, 2016

Answer:

#f(3)=6.#

Explanation:

Given that, #f(n+1)=f(n)-2 rArr f(n+1)-f(n)=-2#

Since, this last eqn. holds good #AA n in NN#, it means that the diff.

of any two consecutive terms of the Seq. is a constant #ne0.#

Obviously, the Seq. has to be an Arithmetic Seq. with, first term

#f(1)=10,# and, the Common Difference #d=-2.#

Accordingly, the General #n^(th)# Term #f(n)#is given by,

#f(n)=f(1)+(n-1)d=10-2(n-1)=12-2n.#

Hence, the Reqd. Term #=f(3)=12-2(3)=6.#

Alternatively,

#f(n+1)=f(n)-2, & f(1)=10.#

#":., by taking "n=1, f(2)=f(1)-2=10-2=8.#

A# For n=2, f(3)=f(2)-2=8-2=6,# As Before!

Enjoy maths.!

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