Question

the sum of the first three terms of an ap is 30.if the product of the extremes is 150.find the ap​

Answer 1

Answer:

Step-by-step explanation:

Let the three terms of AP be a, a+d, a+2d.

Sum of 3 terms is 30

a + a + d + a + 2d = 30

=> 3a + 3d = 30

=> a + d = 10 ---------------> [1]

Product of extreme terms is 150

a * (a+2d) = 150

=> (10 - d) * (10 - d + 2d) = 150 (from [1] : a = 10-d)

=> (10-d)*(10+d) = 150

=> 100 - d² = 150

=> d² = 50

=> d = ±5√2  (Since d = - 5 is not possible)

if d= 5√2                                           | If d = - 5√2

a = 10 - 5√2                                      | a = 10 + 5√2

The AP is 10 - 5√2, 10, 10 + 5√2.   | The AP is 10 - 5√2, 10, 10 - 5√2