Find the three terms of A.P. if the sum of three terms of A.P. is 36 and their product is 528
Answers
Step-by-step explanation:
Given:-
The sum of three terms of A.P. is 36 and their product is 528.
To find:-
Find the three terms of A.P. if the sum of three terms of A.P. is 36 and their product is 528
Solution:-
Let the three terms of an AP be a-d ,a,a+d
The sum of the three terms
= a-d+a+a+d
=>3a
According to the given problem
Sum of the three terms = 36
=>3a = 36
=>a = 36/3
=> a = 12 ------------(1)
Product of the three terms
=>(a-d)(a)(a+d)
=>a(a^2-d^2)
From (1)
=>12(12^2-d^2)
=>12(144-d^2)
According to the given problem
The product of the three terms=528
=>12(144-d^2) = 528
=>144-d^2 = 528/12
=>144-d^2 = 44
=>-d^2 = 44 -144
=>-d^2 = -100
=>d^2 = 100
=>d = ±√100
=>d = ±10
We have a = 12 and d=±10
If a = 12 and d=10 then the three terms of the AP
12-10,12,12+10=2,12,22
If a = 12 and d= -10 then the three terms of the AP
12-(-10),12,12+(-10)
=12+10,12,12-10
=22,12,2
The terms are 2,12,22 or 22,12,2
Answer:-
The three terms of the given AP are 2,12,22 or 22,12,2