Question

the sum of three consecutive terms that are in a. p is 27 and their product is 288. find the three terms.​

Answer 1

Answer:

2, 9, 16 or 16, 9, 2

Step-by-step explanation:

Let the consecutive terms are a - d, a, a + d.

Their sum = 27

⇒ (a - d) + a + (a + d) = 27

⇒ 3a = 27  ⇒ a = 27/3 = 9

Their product = 288

⇒ (a - d)(a)(a + d) = 288

⇒ (9 - d)(9)(9 + d) = 288    {a = 9}

⇒ (9 - d)(9 + d) = 288/9

⇒ 9² - d² = 32    ⇒ 81 - 32 = d²

⇒ 49 = d²             ⇒ ± 7 = d   

terms are 9 - 7,9, 9 + 7 or 9 - (-7), 9, 9 + (-7)

⇒ 2, 9, 16  or 16, 9 , 2

Answer 2

Answer:

Given :-

• The sum of three consecutive terms that are in A.P is 27 and their product is 288.

To Find :-

• What is the three terms.

Solution :-

Let,

$\mapsto$ First consecutive terms be a - d

$\mapsto$ Second consecutive terms be a

$\mapsto$ Third consecutive terms will be a + d

First, we have to find the sum :

$\implies \sf (a - d) + a + (a + d) =\: 27$

$\implies \sf a - d + a + a + d =\: 27$

$\implies \sf a + a + a \cancel{- d} \cancel{+ d} =\: 27$

$\implies \sf 3a =\: 27$

$\implies \sf a =\: \dfrac{\cancel{27}}{\cancel{3}}$

$\implies \sf\bold{\green{a =\: 9}}$

Now, we have to find the product :

$\implies \sf (a - d) \times a \times (a + d) =\: 288$

$\implies \sf 9({a}^{2} - {d}^{2}) =\: 288$

Given :

• a = 9

$\implies \sf 9({9}^{2} - {d}^{2}) =\: 288$

$\implies \sf 9(81 - {d}^{2}) =\: 288$

$\implies \sf 729 - 9{d}^{2} =\: 288$

$\implies \sf - 9{d}^{2} =\: 288 - 729$

$\implies \sf \cancel{-} 9{d}^{2} =\: \cancel{-} 441$

$\implies \sf 9{d}^{2} =\: 441$

$\implies \sf {d}^{2} =\: \dfrac{\cancel{441}}{\cancel{9}}$

$\implies \sf {d}^{2} =\: 49$

$\implies \sf d =\: \sqrt{49}$

$\implies \sf\bold{\pink{d =\: 7}}$

Hence, we get :

• a = 9
• d = 7

Hence, the required three terms are :

$\clubsuit$ First consecutive terms :

$\leadsto \sf a - d$

$\leadsto \sf 9 - 7$

$\leadsto \sf\bold{\red{2}}$

$\clubsuit$ Second consecutive terms :

$\leadsto \sf a$

$\leadsto \sf\bold{\red{9}}$

$\clubsuit$ Third consecutive terms :

$\leadsto \sf a + d$

$\leadsto \sf 9 + 7$

$\leadsto\sf\bold{\red{16}}$

$\therefore$ The three terms are 2,9,16 or 16,9,2.