Question

the sum of first three numbers in an aP is 18 if product of first and thirrd term is five times the common difference find three numbers

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

3 terms are 15 , 6 , -3 or 2 , 6 , 10.

Step-by-step explanation:

Given the sum of first three terms of an AP = 18

Product of 1st and 3rd term is 5 times common difference

we have to find the three numbers.

Let the first three terms of an AP are (a - d) , a , (a + d)

The first term of AP = a - d

And common difference = 2nd term - 1st term = a - ( a - d )

                                                                            = a - a + d = d

Sum of first three term of AP = 18

⇒ ( a - d ) + ( a ) + ( a + d ) = 18

⇒  a - d + a + a + d = 18

⇒  3a = 18 ⇒ a = 6

Now, Product of 1st and 3rd term is 5 times common difference

⇒ $(a-d)\times (a+d)=5\times d$

⇒ $a^2-d^2=5d$    ( using identity, ( x - y )( x + y ) = x² - y² )

⇒ $6^2-d^2=5d$

⇒ $d^2+5d-36=0$

⇒ $d^2+9d-4d-36=0$

⇒ $d(d+9)-4(d+9)=0$

⇒ $(d-4)(d+9)=0$

⇒ $d=4, d=-9$

when d = -9

⇒ $a-d=6-(-9)=15, a=6, a+d=6-9=-3$

when d = 4

⇒ $a-d=6-4=2, a=6, a+d=6+4=10$

Therefore, 3 terms are 15 , 6 , -3 or 2 , 6 , 10.