Question

the number are in AP if their sum is 27 and the product is 648 find the number​

Answer 1

Answer:

let the numbers be x-y,x,x+y

then x-y+x+x+y=27

3x=27

x=9

(x-y)(x)(x+y)=648

(xsquare-ysquare)(x)=648

(9square-ysquare)(9×9)=648

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y=3

Answer 2

Answer:

Given: Sum of first three terms is 27

Let us assume the first three terms as

a – d, a, a + d [where a is the first term and d is the common difference]

So,

sum of first three terms is a – d + a + a + d

= 27 3a = 27 a = 9

It is given that the product of three terms is 648

So,

a³ – ad²= 648

Substituting the value of a = 9,

we get 9³– 9d²= 648

729 – 9d² = 648

81 = 9d²

d = 3 or d = – 3

Hence, the given terms are a – d, a, a + d which is 6, 9, 12.