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Directions for the following two questions:Let $$a_1= p$$ and $$b_1 = q$$, where p and q are positive quantities.Define $$a_n = pb_{n-1} , b_n = qb_{n-1}$$ , for even n > 1. and $$a_n = pa_{n-1} , b_n = qa_{n-1}$$ , for odd n > 1.Which of the following best describes $$a_n + b_n$$ for even n?
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By: anil on 05 May 2019 02.29 am
$$a_n + b_n$$ for even n = $$p*b_{n-1} + q*b_{n-1}$$ = $$(p+q)*b_{n-1}$$
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$$b_{n-1} = q*a_{n-2} = qp*b_{n-3}$$
= $$q^2*p*a_{n-4} = q^2p^2*b_{n-5}$$
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= $$(qp)^{n/2-1}*b_1 = (qp)^{n/2-1}*q$$
So, $$a_n + b_n$$ = $$q(pq)^{(n/2) -1}(p+q)$$