Question

The sum of three terms in an AP is 33 and their product is 155. Find the terms​

Answer 1

Correct Question:

The sum of three terms in an AP is 33 and their product is 1155. Find the terms.

Answer:

In an AP:

When a = 11 and d = + 4

• Terms: 7, 11, 15

When a = 11 and d = - 4

• Terms: 15, 11, 7

Step-by-step explanation:

Given that:

• The sum of three terms in an AP is 33.
• Their product is 1155.

To Find:

• What are these terms?

Let us assume:

• First term = (a - d)
• Second term = a
• Third term = (a + d)

According to the question.

Sum of three terms = 33

⟶ (a - d) + a + (a + d) = 33

⟶ a - d + a + a + d = 33

Cancelling d.

⟶ 3a = 33

⟶ a = 33/3

⟶ a = 11

Products of these terms = 1155

⟶ (a - d) × a × (a + d) = 1155

Substituting the value of a.

⟶ (11 - d) × 11 × (11 + d) = 1155

⟶ (11 - d) × (11 + d) = 1155/11

⟶ (11 - d) × (11 + d) = 105

Applying algebraic identities.

⟶ 11² - d² = 105

⟶ 121 - d² = 105

⟶ d² = 121 - 105

⟶ d² = 16

⟶ d = √16

⟶ d = ± 4

We have:

• The value of a = 11
• The value of d = ± 4

When d = + 4

• First term = (a - d) = (11 - 4) = 7
• Second term = a = 11
• Third term = (a + d) = (11 + 4) = 15

When d = - 4

• First term = (a - d) = 11 - (- 4) = 11 + 4 = 15
• Second term = a = 11
• Third term = (a + d) = 11 + (- 4) = 11 - 4 = 7

Answer 2

refer attachment

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