Question

the sum of the number in ap is 18 if the product of first and third no.is five times the common difference. find the number​

Answer 1

Answer:

The A.P. will be 2, 6, 10, 14,........

The 3 numbers will be 2, 6 and 10

Step-by-step explanation:

Your Queation must be

"The sum of first three numbers in an AP is 18. If the product of the first and the third term is 5 times the

common difference find the three numbers"

Let the A.P be (a - d), a, (a + d),......

According to the Question,

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

a - d + a + a + d = 18

3a = 18

a = 18/3

a = 6

Now, according to the Question,

(a - d)(a + d) = 5 × d

a² - d² = 5d

6² - d² = 5d

36 - d² = 5d

d² + 5d - 36 = 0

Sum = 5

Product = -36

factors are 9 and -4

d² + 9d - 4d - 36 = 0

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

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

so, d = -9 or d = 4

Now, if we put d = -9 we get AP = 2, -7, -16,......

But the first 3 three terms don't add upto 18 so, d = 4

So, the A.P. will be 2, 6, 10, 14,........

Hope it helped and you understood it........All the best