1.

Write the first five terms of the sequence defined by an=(-1)^n-1.2^n

Answer»

The answer is given below :

The sequence is defined as

an = (-1)^(n - 1) × 2^n, where n is any Natural number

Now, putting n = 1, 2, 3, 4, 5, ... we will GET the RESULTING sequence.

When n = 1,
a1 = (-1)^(1-1) × 2^1 = (-1)^0 × 2 = 1 × 2
= 2

When n = 2,
a2 = (-1)^(2-1) × 2^2 = (-1)^1 × 4 = -1 × 4
= -4

When n = 3,
A3 = (-1)^(3-1) × 2^3 = (-1)^2 × 8 = 1 × 8
= 8

When n = 4,
a4 = (-1)^(4-1) × 2^4 = (-1)^3 × 16 = -1 × 16
= -16

When n = 5,
a5 = (-1)^(5-1) × 2^5 = (-1)^4 × 32 = 1 × 32
= 32

Thus, the first five of the given sequence are
2, -4, 8, -16, 32

Thank you for your question.


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