Question

In an AP 4th term and 8th term are in the ratio 1:2 If the 10th term is 30.Find the AP​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

• 3, 6, 9, 12, 15.. is the A.P

Step-by-step explanation:

Given :

In a A.P: 4rh, 8th term are in the ratio 1 : 2.

10th term in 30.

To find :

The A.P ?

Solution :

We have,

⇒ a₄ = 1

⇒ a₈ = 2

• a₄ : a₈ = 1 : 2

Hence,

• [a₄] = a + 3d
• [a₈] = a + 7d

According to the question,

⇒ (a + 3d)/(a + 7d) = 1/2

⇒ 2(a + 3d) = 1(a + 7d)

⇒ 2a + 6d = a + 7d

⇒ 2a - a = 7d - 6d

⇒ a = d

Also given,

⇒ a₁₀ = 30

Hence,

• [a₁₀] = a + 9d = 30

⇒ a + 9d = 30

⇒ a + 9(a) = 30

⇒ 10a = 30

⇒ a = 30/10

⇒ a = 3

Now, the A.P will be,

• a, a + d, a + 2d, a + 3d, a + 4d

Hence,

⇒ 3, 3 + 3, 3 + 2 × 3, 3 + 3 × 3, 3 + 4 × 3...

⇒ 3, 6, 3 + 6, 3 + 9, 3 + 12....

⇒ 3, 6, 9, 12, 15..

∴ 3, 6, 9, 12, 15.. is the required A.P