InterviewSolution
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InterviewSolution
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In illustration 13, if `a_(4) = 28, "then" p + 2q =`A. 21B. 11C. 7D. 12 |
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Answer» Correct Answer - D From illustration 13, we obtain `a_(n+1) = a_(n) + a_(n-1)" "...(i)` `rArr" "a_(4) = a_(3) + a_(2)" "["Putting n = 3"]` `rArr" "a_(4) = (a_(2)+a_(1)) + (a_(1) + a_(0))" ["Putting n = 2, 1 in (i)"]` `rArr" "a_(4) = a_(2) + 2a_(1) + a_(0)` `rArr" "a_(4) = (a_(1) + a_(0)) + (2a_(1) + a_(0))" "["Putting n = 1 in (i)", a_(2) = a_(1) + a_(0)]` `rArr" "a_(4) = 3a_(1) + 2a_(0)` ltbgt `rArr" "28 = 3 (p alpha+q beta) + 2(p+q)" "[therefore a_(n) = p alpha^(n) + q beta^(n)]` `rArr" "28 = 3p ((1+ sqrt(5))/(2))+3q((1- sqrt(5))/(2))+2(p+q)" "[therefore alpha = (1+sqrt(5))/(2), beta = (1-sqrt(5))/(2)]` `rArr" "28 = (7)/(2)(p+q)+(3 sqrt(5))/(2) (p-q)` `rArr" "(7)/(2)(p+q) = 28 and p - q = 0` `rArr" "p + q = 8 and p = q rArr p = q = 4` Hence, p + 2q = 4 + 8 = 12. |
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