Question

If 2009ap inserted between 3 and 4023 then the 1004th AP is

Answer 1

Step-by-step explanation:

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Answer 2

Complete question:

If 2009 arithmetic means inserted between 3 and 4023 then the 1004th AP is

Answer:

1004th term is 2009.

Step-by-step explanation:

Assumption,

Let the common difference of the AP be 'd'

Given,

$3, a_1, a_2....a_{2009}, 4023$ are in AP.

The first term of AP (a) = 3

The last term of AP (aₙ) = 4023

The total number of terms in the given AP (n) = 2011

To find,

1004th term in the following AP(a₁₀₀₄).

Calculation,

We know that

aₙ = a + (n - 1)d

⇒ 4023 = 3 + (2011 - 1)d

⇒ 4020 = 2010 × d

⇒ d = 2

Now for finding the 1004th term

i.e. a₁₀₀₄ we have to take the value of n to be 1004

So in equation (1) we have to substitute a = 3, aₙ = a₁₀₀₄, n = 1004, d = 2

⇒ a₁₀₀₄ = 3 + (1004 - 1) × 2

⇒ a₁₀₀₄ = 3 + 2006

⇒ a₁₀₀₄ = 2009

Therefore, 1004th term is 2009.

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