List the first five terms of the sequence. an = (-1)ⁿ - (1.5)ⁿ.

Solution:

Given, the formula is aₙ = (-1)ⁿ - (1.5)ⁿ.

We have to write the first five terms of the sequence.

For first term n = 1

a₁ = (-1)¹ - (1.5)¹

= -1 - 1.5

= -2.5

For second term n = 2

a₂ = (-1)² - (1.5)²

= 1 - 2.25

= -1.25

For third term n = 3

a₃ = (-1)³ - (1.5)³

= -1 - 3.375

= -4.375

For fourth term n = 4

a₄ = (-1)⁴ - (1.5)⁴

= 1 - 5.0625

= -4.0625

For fifth term n = 5

a₅ = (-1)⁵ - (1.5)⁵

= -1 - 7.59375

= -8.59375

Therefore, the first five terms of the sequence are -2.5, -1.25, -4.375, -4.0625 and -8.59375.

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List the first five terms of the sequence. an = (-1)ⁿ - (1.5)ⁿ.

Summary:

The first five terms of the sequence given by the formula an = (-1)ⁿ - (1.5)ⁿ are -2.5, -1.25, -4.375, -4.0625 and -8.59375 respectively.