Question

Sum of first three terms of Arithmetic progression is 18. If the product of first and third term is five times the common difference find three numbers

Answer 1

Here is the answer

Hope it helps.

Answer 2

Answer: The three numbers are 15,6,-3 and 2,6,10.

Step-by-step explanation:

Since we have given that

The three terms of Arithmetic progressions are

a-d,a,a+d.

So, Product of first and third term is five times the common difference and the sum of first three terms is 18.

According to question, it becomes,

$a-d+a+a+d=18\\\\3a=18\\\\a=\frac{18}{3}\\\\a=6$

and

$(a-d)(a+d)=5d\\\\a^2-d^2=5d\\\\6^2-d^2=5d\\\\36-d^2=5d\\\\d^2+5d-36=0\\\\d^2+9d-4d-36=0\\\\d(d+9)-4(d+9)=0\\\\(d+9)(d-4)=0\\\\d=-9,4$

So, three numbers will be

a-d,a,a+d=6-(-9),6,6-9=15,6,-3

and 6-4,6,6+4=2,6,10