Find the first four terms of the sequence an = cos (nπ / 2)?

Given:

The sequence is defined as a_n = cos(nπ / 2).

We need to find the first four terms of the sequence.

Concept Used:

The formula for cosine is used to calculate the terms of the sequence by substituting n = 1, 2, 3, and 4 into the formula cos(nπ / 2).

The cosine values for some standard angles are:

• cos(0) = 1

• cos(π/2) = 0

• cos(π) = -1

• cos(3π/2) = 0

Calculation:

Substitute the values of n:

For n = 1:

  a₁ = cos(1 × π / 2) = cos(π/2) = 0

For n = 2:

  a₂ = cos(2 × π / 2) = cos(π) = -1

For n = 3:

  a₃ = cos(3 × π / 2) = cos(3π/2) = 0

For n = 4:

  a₄ = cos(4 × π / 2) = cos(2π) = 1

Conclusion:

∴ The first four terms of the sequence are:

a_n = 0, -1, 0, 1

Therefore, the correct answer is Option (4).