Which of the following list of numbers form A.R's? If they form an A.P

1.	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.a, 2a, 3a, 4a, ....
Answer» We have, a₂ – a₁ = 2a – a = a a₃ – a₂ = 3a – 2a = a a₄ – a₃ = 4a – 3a = a 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 = a Now, we have to find the next three terms. We have a₁ = a, a₂ = 2a, a₃ = 3a and a₄ = 4a Now, we will find a₅, a₆ and a₇ So, a₅ = 4a + a = 5a a₆ = 5a + a = 6a and a₇ = 6a + a = 7a Hence, the next three terms are 5a, 6a and 7a

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.a, 2a, 3a, 4a, ....

Answer»

We have,

a₂ – a₁ = 2a – a = a

a₃ – a₂ = 3a – 2a = a

a₄ – a₃ = 4a – 3a = a

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 = a

Now, we have to find the next three terms.

We have a₁ = a, a₂ = 2a, a₃ = 3a and a₄ = 4a

Now, we will find a₅, a₆ and a₇

So, a₅ = 4a + a = 5a

a₆ = 5a + a = 6a

and a₇ = 6a + a = 7a

Hence, the next three terms are 5a, 6a and 7a