Write the first terms of the sequences whose nth term are:an = (-1)n2

1.	Write the first terms of the sequences whose nth term are:an = (-1)n2n
Answer» Given sequence whose a_n = (-1)ⁿ2ⁿ To get first five terms of the sequence, put n = 1, 2, 3, 4, 5 in the above. a₁ = (-1)¹.2¹ = (-1).2 = -2 a₂ = (-1)².2² = (-1).4 = 4 a₃ = (-1)³.2³ = (-1).8 = -8 a₄ = (-1)⁴.2⁴ = (-1).16 = 16 a₅ = (-1)⁵.2⁵ = (-1).32 = -32 ∴ The first five terms of the sequence are – 2, 4, – 8, 16, – 32.

Write the first terms of the sequences whose nth term are:an = (-1)n2n

Answer»

Given sequence whose a_n = (-1)ⁿ2ⁿ

To get first five terms of the sequence, put n = 1, 2, 3, 4, 5 in the above.

a₁ = (-1)¹.2¹ = (-1).2 = -2

a₂ = (-1)².2² = (-1).4 = 4

a₃ = (-1)³.2³ = (-1).8 = -8

a₄ = (-1)⁴.2⁴ = (-1).16 = 16

a₅ = (-1)⁵.2⁵ = (-1).32 = -32

∴ The first five terms of the sequence are – 2, 4, – 8, 16, – 32.