Which of the following list of numbers form A.R's? If they form an A.P., find the common difference d and also write its next three terms.

1, - 1, - 3, - 5,

We have,

a₂ – a₁ = -1 – 1 = -2

a₃ – a₂ =-3 – (-1) = -3 + 1 = -2

a₄ – a₃ =-5 – (-3) = -5 + 3= -2

i.e. a_k+1 – a_k is the same every time.

So, the given list of numbers forms an AP with the common difference d = -2

Now, we have to find the next three terms.

We have a₁ = 1, a₂ = -1, a₃ = -3 and a₄ = -5

Now, we will find a₅, a₆ and a₇

So, a₅ = -5 + (-2) = -5 – 2 = -7

a₆ = -7 + (-2) = -7 – 2 = -9

and a₇ = -9 + (-2) = -9 – 2 = -11

Hence, the next three terms are -7, -9 and -11