Question

The population of cattle in a farm increases so that the difference between the population in year n+2 and that in year n is proportional to the population in n + 1. If the populations in years 2010, 2011 and 2013 were 39, 60 and 123, respectively, then the population in 2012 was

• A. 81
• B. 84
• C. 87
• D. 90

Answer 1

The correct option is B

84

Year Population

2010 ---------39

2011 --------- 60

2012 --------- x

2013 ---------- 123

According to Q

x - 39 = k (60) & 63 = kx

⇒ x – 39= $\frac{63}{x}.60$

⇒ $x^2$ - 39x - (60)(63) = 0

x = 84 & - 40