Show that the sequence defined by an = 3n2 - 5 is not A.P.

1.	Show that the sequence defined by an = 3n2 - 5 is not A.P.
Answer» Given: The sequence a_n = 3n² - 5. To prove: the sequence defined by a_n = 3n² - 5 is not A.P. Proof: Consider the sequence a_n = 3n² - 5, Put n = 1 a₁= 3(1)² – 5 = 3 – 5 = -2 Put n = 2 a₂= 3(2)² – 5 = 12- 5 = 7 Put n = 3 a₃= 3(3)² – 5 = 27 – 5 = 22 In an A.P the difference of consecutive terms should be same. So, Common difference, d₁= a₂– a₁ =7 – (-2) = 9 Common difference, d₂ = a₃ – a₂ = 22 – 9 = 13 Since, d₁ ≠ d₂ Therefore, it’s not an A.P.

Answer»

Given:

The sequence a_n = 3n² - 5.

To prove:

the sequence defined by a_n = 3n² - 5 is not A.P.

Proof:

Consider the sequence a_n = 3n² - 5,

Put n = 1

a₁= 3(1)² – 5 = 3 – 5 = -2

Put n = 2

a₂= 3(2)² – 5 = 12- 5 = 7

Put n = 3

a₃= 3(3)² – 5 = 27 – 5 = 22

In an A.P the difference of consecutive terms should be same.

So,

Common difference, d₁= a₂– a₁ =7 – (-2) = 9

Common difference, d₂ = a₃ – a₂ = 22 – 9 = 13

Since, d₁ ≠ d₂

Therefore, it’s not an A.P.

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