Question

the sum of three consecutive terms is 15 and their product is 45​

Answer 1

Step-by-step explanation:

the ap can be written as (a-d), a ,(a+d). we can write like this because the terms still have a difference of d.

their sum is 15, therefore (a-d)+a+(a+d) = 15

3a = 15

a = 5.

now their product is 45. therefore

(5-d)(5)(5+d) = 45

(5) [(5-d)(5+d)] = 45

5 × [25-d²]= 45

25-d² = 9

d²= 25-9

d = +or- 4

therefore the ap when d is +4 is (5-4),(5),(5+4). i.e 1, 5, 9

the ap when d = -4 is [5-(-4)] , 5, [5+(-4)]

i.e 9, 5, 1.