Sequences & Series
AP sets with sum and product
nta_pyq_2025_apr
Grade 12
Question:
Consider two sets A and B, each containing three numbers in A.P. Let the sum and the product of the elements of A be 36 and p respectively and the sum and the product of the elements of B be 36 and q respectively. Let d and D$p+q$be the common differences of AP's in A and B respectively such that$D = d + 3$,$d > 0.$If$p-q = 19$5, then$p - q$is equal to
Step-by-Step Solution
Key Concept: Write each$three-number$AP as$a-d,a,a+d$and use sum and product constraints for both sets.
Let A($a - d$, a,$a + d)$B($b - D$, b,$b + D)$$(4)$$a = 12$$b = 12$2$p = 12$($144 - d$) 2$q = 12$($144 - D$)$p+q$$19 = p-q$5 p 24 12 = = q 14 7 2$144 - d$$12 = 2$$144 - (d + 6d + 9)$7 2 2$1008 - 7d$= -$12d - 72d + 1620$2$5d + 72d - 612 = 0$$d = 6$$D = 9$2 3$p - q = 12$($D - d$) = 12($81 - 36) = 12$(45)$= 540$option$(4)$
Correct Answer: 4