In a mango groove the trees are planted in horizontal rows. THERE ARE 6 TREES MORE IN EACH HORIZONTAL ROW. Altogether there are 720 trees. Find the number of trees in horizontal rows.
This is a problem is AP, where the sum is 720 and d= 6. Both a and n are unknown. Let n = number of rows and a = number of trees in the first row.
Sn = (n/2)[2a+(n-1)d], or
720 = (n/2)[2a+(n-1)6], or
720 = n[a+(n-1)3], or
720 = an +3n(n-1) = 3n^2 +(a-3)n
3n^2 -(3-a)n - 720 = 0 …(1)
If a = 3, n = (720/3)^0.5 = 15.5. Rejected
If a = 6, (1) becomes 3n^2 -(3–6)n - 720 = 0 or
3n^2 +3n - 720 = 0 or
n^2+n-240=0
(n+16)(n-15) = 0
Or n = 15 and as a negative value of n = -16 is inadmissible.