The three numbers will be 12, 7, 2 and 3, 7, 11.
<h3>What is a sequence?</h3>A sequence is a list of elements that have been ordered in a sequential manner, such that members come either before or after.
Let the three consecutive numbers be a, a + d, and a + 2d
The sum of three numbers which are consecutive terms of an A.P. is 21.
a + a + d + a + 2d = 21
3(a + d) = 21
a = 7 - d
If the second number is reduced by 1 and the third term is increased by 1 we obtain the geometric product.
Then the number will be a, a + d − 1, a + 2d + 1. Then we have
On simplifying, we have
36 = a (8 + d)
a² - 15a + 36 = 0
On factorizing, the value of a will be
a² - 15a + 36 = 0
a² - 12a - 3a + 36 = 0
(a - 12)(a - 3) = 0
a = 3, 12
If a = 12, then the value of d will be
d = 7 - 12
d = -5
If a = 3, then the value of d will be
d = 7 - 3
d = 4
Then the three numbers will be 12, 7, 2 and 3, 7, 11.
More about the sequence link is given below.
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