Question

The sum of the first three numbers in an ap is 18.If the product of first and third term is 5times the common difference.Find the three numbers

Answer 1

Answer:

The three numbers are either 2,6,10 or 15,6,-3.

Step-by-step explanation:

Let first three numbers in an AP are a-d, a,a+d. Where d is common difference.

It is given that the  sum of the first three numbers in an ap is 18.

$(a-d)+a+(a+d)=18$

$3a=18$

$a=6$

The product of first and third term is 5 times the common difference.

$(a-d)(a+d)=5d$

$a^2-d^2=5d$

$(6)^2-d^2=5d$

$d^2+5d-36=0$

$d^2+9d-4d-36=0$

$d(d+9)-4(d+9)=0$

$(d-4)(d+9)=0$

$d=4,-9$

If a=6 and d =4, then the three terms are 2,6,10.

If a=6 and d =-9, then the three terms are 15,6,-3.

Therefore the three numbers are either 2,6,10 or 15,6,-3.

Answer 2

Answer:

u will get two ap cases as d will be positive and negative.

Step-by-step explanation:

hope this helps you.