Question

The sum of 3 terms of an AP is 21 and their product is 280. find the terms?

Answer 1

Sum of 3 terms of A.P = 21
⇒ n = 3, S = 21
S = n/2 (2 a+(n-1)d)
21 = 3/2 (2a +2d)
21 = 3(a+d)
⇒ a+d = 7 ⇒ d = 7-a
Product is 280
a*(a+d)*(a+2d) = 280
a* 7 * (a+2d) = 280
a² + 2ad = 40
a² + 2a(7-a) = 40
a² + 14a - 2a² = 40
-a² + 14a - 40 = 0
a² - 14a + 40 = 0
a² - 10a - 4a + 40 = 0
a(a-10)-4(a-10) = 0
(a-10)(a-4) = 0
⇒a=10 or a=4
if a=10, d= -3 and if a=4,d= 3
terms of A.P are 10,7,4 or 4,7,10