each year for 4 years, a farmer increased the number of trees in a certain orchard by 1 / 4 of the number of trees in the orchard of the preceding year. if all of the trees thrived and there were 12500 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period.  Choose the correct choice from the following.
A) 5113 B) 5117 C) 5120 D) 8119 E) 10115
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/4) + 1</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">(5/4) ** 4</gadget>
<output>625/256 = around 2.441406</output>

<gadget id="calculator">12_500 / (625/256)</gadget>
<output>5_120</output>

<result>C</result>
each year for 4 years, a farmer increased the number of trees in a certain orchard by 1 / 4 of the number of trees in the orchard of the preceding year. if all of the trees thrived and there were 12500 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period.
divide(12500, power(add(divide(1, 4), 1), 4))
"trees increase by 1 / 4 the number of trees in preceding year . hence , correct answer must be divisible by 4 . based on divisibility rules , if last 2 digits are divisible by 4 then the number is divisible by 4 . thus , we can eliminate a , b , d , e the answer to be c again , trees increase by 1 / 4 the number of trees in preceding year . hence , the number of trees increase by 5 / 4 times the number of trees the preceding year . if x = initial number of trees = 5120 year 1 = 5 / 4 x year 2 = ( 5 / 4 ) ( 5 / 4 ) x year 3 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x year 4 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x only for answer d : ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) 5120 = 12500 hence , correct answer = c"