Question

The sum of the first three terms of an AP is 36 and their product is 1620. Find the AP.

Answer 1

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Answer 2

Answer:

9, 12, 15

Step-by-step explanation:

Define the 3 terms:

Let the 3 terms be (x - d), x and (x + d)

The sum is 36:

(x - d) + x + (x + d) = 36

x - d + x + x + d = 36

3x = 36

x = 36 ÷ 3

x = 12

Their product is 1620:

x(x - d)(x + d) = 1620

x(x² - d²) = 1620

Solve d:

Sub x = 12 into x(x² - d²) = 1620

12(12² - d²) = 1620

12² - d² = 135

d² = 144 - 135

d² = 9

d = 3

Find the AP:

First term = x - d = 12 - 3 = 9

Second term = x = 12

Third term = x + d = 12 + 3 = 15

Therefore the AP is : 9, 12, 15

Answer: 9, 12, 15