Question

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Answer 1

Answer:

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Answer 2

Question:

Find the A.P. whose 6th term is 5 and 10th term is 9.

Answer:

The required AP is 0, 1, 2, 3, ...

Step-by-step-explanation:

We have given that,

For an AP,

• t₆ = 5
• t₁₀ = 9

We have to find the AP.

Now, we know that,

tₙ = a + ( n - 1 ) * d - - - [ Formula ]

∴ t₆ = a + ( 6 - 1 ) * d

⇒ 5 = a + 5d

⇒ a + 5d = 5 - - - ( 1 )

Now,

t₁₀ - t₆ = 4d

⇒ 9 - 5 = 4d

⇒ 4 = 4d

⇒ d = 4 ÷ 4

⇒ d = 1

∴ Common difference = 1

By substituting this value in equation ( 1 ), we get,

a + 5d = 5

⇒ a = 5 - 5d

⇒ a = 5 - 5 * 1

⇒ a = 5 - 5

⇒ a = 0

∴ First term = 0

Now,

First term = a = 0

Second term = a + d = 0 + 1 = 1

Third term = a + 2d

⇒ 0 + 2 * 1

⇒ 0 + 2

⇒ Third term = 2

Fourth term = a + 3d

⇒ 0 + 3 * 1

⇒ 0 + 3

⇒ Fourth term = 3

∴ The required AP is 0, 1, 2, 3, ...