Question

the sum of 3numbers in A. p the product of 1st and last is 56 find the numbers​

Answer 1

AnsWer :

4 , 9 , 14.

Correct QuestioN :

The sum of three number in AP is 27. The product of first and last number is 56. Find the number.

To FinD :

Find the number.

SolutioN :

Let,

• The three number in AP be
• a - d , a , a + d.

Case 1.

• The sum of three number in AP is 12.

→ a - d + a + a + d = 12.

→ 3a = 27.

→ a = 27 /3.

→ a = 9.

$\rule{90}2$

Case 2.

• The product Of 1st and last term of given AP is 56.
• a - d → First number.
• a + d → Last number.

→ a - d * a + d = 56.

→ ( a + d )( a - d ) = 56.

→ a² - d² = 56.

→ ( 9 )² - d² = 56.

→ 81 - d² = 56.

→ - d² = 56 - 81.

→ - d² = - 25.

→ d² = 25.

→ d = ± 5.

$\rule{90}2$

So,

Our Number in AP → a - d , a , a + d.

★ When,

• a = 9.
• d = 5.

→ 9 - 5 , 9 , 9 + 5.

→ 4 , 9 , 14.

★ When,

• a = 9.
• d = - 5.

→ 9 + 5 , 9 , 9 - 5.

→ 14 , 9 , 4.

Therefore, the number is 4 , 9 , 14.