Question

In an A.P., the sum of three consecutive terms is 24 and their product is 312.
Complete the following activity to find the terms. (The terms in A.P. are in
ascending order).​

Answer 1

here at is 8,8+10root2 .....

Answer 2

The three terms of an arithmetic progression in ascending order are 3, 8 and 13.

Step-by-step explanation:

Let three terms of an arithmetic progression = (a - d), a, ( a + d)

To find, the three terms of an arithmetic progression = ?

According to question,

The sum of three terms of an arithmetic progression = 24

∴  (a - d) + a + ( a + d) = 24

⇒ 3a = 24

⇒ a = 8

Also, The product of three terms of an arithmetic progression = 312

∴  (a - d)a( a + d) = 312

⇒ $a(a^{2}-d)^{2} =312$

Put a = 8, we get

⇒ $8(8^{2}-d^2)=312$

⇒ $64 - d^{2} = 39$

⇒ $d^{2} = 64 - 39 = 25$

⇒ d = ± 5

∴ a = 8 and d = ± 5

Put a = 8 and d = 5

∴ Three terms of an arithmetic progression = (8 - 5), 8 and ( 8 + 5)

= 3, 8 and 13

Thus, the three terms of an arithmetic progression in ascending order are 3, 8 and 13.