The general term of a sequence is given by an = - 4n2 + 15.Is the sequ

1.	The general term of a sequence is given by an = - 4n2 + 15.Is the sequence an A.P..? If so, find its 15th term and the common difference.
Answer» Put n = 1 a₁= - 4(1)² + 15 = 11 Put n = 2 a₂= - 4(2)²+ 15 = -1 Put n = 3 a₃= - 4(3)² + 15 = -21 Common difference, d₁= a₂ – a₁ = -1 – 11 = -12 Common difference, d₂= a₃ – a₂ = - 21 + 1 = 20 Since, d₁ ≠ d₂ Therefore, it’s not an A.P

The general term of a sequence is given by an = - 4n2 + 15.Is the sequence an A.P..? If so, find its 15th term and the common difference.

Answer»

Put n = 1

a₁= - 4(1)² + 15 = 11

Put n = 2

a₂= - 4(2)²+ 15 = -1

Put n = 3

a₃= - 4(3)² + 15 = -21

Common difference, d₁= a₂ – a₁ = -1 – 11 = -12

Common difference, d₂= a₃ – a₂ = - 21 + 1 = 20

Since, d₁ ≠ d₂

Therefore, it’s not an A.P