Question

6. Find three numbers in AP whose sum is 15 and product is 80.
HINT- Let the numbers be (a-d), a, (a+d).​

Answer 1

Step-by-step explanation:

a-d+a+a+d =15

3a =15

a =5

(a-d)(a)(a+d) =80

(a^2-d^2)5 =80

a^2 - d^2 = 80/5

5^2 - d^2 =16

-d^2 = 16/25

d =4 /5

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Answer 2

Answer: let the three numbers in AP be (a-d),a,(a+d)

According to question,

Sum of terms=15

a-d+a+a+d=15

3a=15

a=5

Product of terms=80

(a-d) X a X (a+d)=80

(a^2-d^2)a=80

Putting the value of a, we have

(25-d^2)5=80

25-d^2=16

25-16=d^2

9=d^2

d=3

So the terms are: a-d= 5-3=2

a=5

a+d=5+3=8

A.P.=2,5,8