Question

The sum of three terms of an arithmetic progression is 39 and their product is 1872 find the terms

Answer 1

therefore the terms are

8,13,18......

Answer 2

The three terms of an arithmetic progression are (8, 13 and 18) or, (18, 13 and 8).

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 = 39

∴  (a - d) + a + ( a + d) = 39

⇒ 3a = 39

⇒ a = 13

Also, The product of three terms of an arithmetic progression = 1872

∴  (a - d)a( a + d) = 1872

⇒ a($a^{2}-d)^{2}$ =  1872

Put a = 13, we get

⇒ 13($13^{2}-d^2)=1872$

⇒ 169 - $d^{2}$ = 144

⇒ $d^{2}$ = 169 - 144 = 25

⇒ d = ± 5

∴ a = 13 and d = ± 5

Put a = 13 and d = 5

Three terms of an arithmetic progression = (13 - 5), 13 and ( 13 + 5)

= 8, 13 and 18

Put a = 13 and d = - 5

Three terms of an arithmetic progression = (13 + 5), 13 and ( 13 - 5)

= 18, 13 and 8

Thus, the three terms of an arithmetic progression are (8, 13 and 18) or, (18, 13 and 8).