Question

The sum of three numbers in AP is 18. If the product of first and t
number is five times the common difference, find the numbers.
BSE​

Answer 1

Step-by-step explanation:

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

⇒

⇒    ( using identity, ( x - y )( x + y ) = x² - y² )

⇒

⇒

⇒

⇒

⇒

⇒

when d = -9

⇒

when d = 4

⇒

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

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