Answer: n = 16
Step-by-step explanation:
Formula for finding the sum of an AP
Sₙ = ⁿ/₂ {(2a + ( n - 1 )d )}
where a = 8, d is 4 months = ¹/₃ of a year and ₎ and Sₙ = 168
Therefore, substitute for the values an form an equation with it
168 = ⁿ/₂{( 2(8) + ( n - 1 )¹/₃}
multiply by 2 to make it a linear expression
336 = n( 16 + ⁿ/₃ - ¹/₃ )
336 = n( 16 - ¹/₃ + ⁿ/₃ )
336 = n( 48 - 1 /3 + ⁿ/₃
Now open the brackets
336 = n(⁴⁷/₃ + ⁿ/₃ )
336 = ⁴⁷ⁿ/₃ + n²/₃
Multiply through by 3
1,008 = 47n + n², then rearrange
n² + 47n - 1008 = 0
n² + 63n - 16n - 1008 = 0
factorize the expression by grouping
n(n + 63) - 16(n + 63) = 0
pick common factors
(n + 63)(n - 16) = 0
therefore n = -63 or 16. But note that n ≠ -63,
Therefore n = 16 which is the required number of boys in the class.
