Question

What will be the 6^th, 12^th and 25^th term of the sequence defined by a_n = (n – 2)² + 2n?

Answer 1

Given: a_n = (n – 2)² + 2n

To find the 6^th term, put n = 6

∴ a₆ = (6 – 2)² + 2(6)

= (4)² + 12

= 16 + 12

= 28

To find the 12^th term, put n = 12

∴ a₁₂ = (12 – 2)² + 2(12)

= (10)² + 24

= 100 + 24

= 124

To find the 25^th term, put n = 25

∴ a₂₅ = (25 – 2)² + 2(25)

= (23)² + 50

= 529 + 50

= 579

Hence, the 6^th, 12^th and 25^th term of the sequence are 28, 124 and 579 respectively.