Question

If a_n represents n^th term of the A.P. `- 15/4, - 10/4, - 5/4,` ...... then value of a₁₆ – a₁₂ is ______.

Options

• 4

• `5/4`

• 5

• `25/4`

Answer 1

If a_n represents n^th term of the A.P. `- 15/4, - 10/4, - 5/4,` ...... then value of a₁₆ – a₁₂ is 5.

Explanation:

1. Identify given values

From the given Arithmetic Progression (A.P.) `- 15/4, - 10/4, - 5/4,` ......, we can

First term (a) = `- 15/4`

Common difference (d) = a₂ – a₁

= `- 10/4 - (- 15/4)`

= `5/4`

2. Express terms using the formula

The n^th term of an A.P. is given by a_n = a + (n – 1)d.

a₁₆ = a + 15d

a₁₂ = a + 11d

3. Calculate the difference

Subtracting the two terms:

a₁₆ – a₁₂ = (a + 15d) – (a + 11d)

a₁₆ – a₁₂ = 4d

Substituting the value of d:

`a_16 - a_12 = 4 xx 5/4`

a₁₆ – a₁₂ = 5

The value of a₁₆ – a₁₂ is 5.