The n^{\;{th }\;} term of the sequence -1,2,-4,8,.is

Correct Answer is : (−1)n2n−1(-1)ⁿ 2ⁿ-1}(−1)n2n−1

Correct Answer is : (−1)n2n−1(-1)ⁿ 2ⁿ-1}(−1)n2n−1

Test Index

Sequence and Series

Question : 76 of 86

Marks: +1, -0

The

n^{\;\text{th }\;}

-1,2,-4,8,

.is

Solution:

Concept:

The sequence alternates signs and doubles in magnitude each step.

Explanation:

The terms are:

T_1 = -1

T_2 = 2

T_3 = -4

T_4 = 8

The absolute values follow

1, 2, 4, 8, \dots

which is

2^{n-1}

The signs alternate:

-, +, -, +, \dots

which is

(-1)^n

(since first term is negative).

Thus the

n^{\text{th}}

term is

(-1)^n \cdot 2^{n-1}

Answer:

Option A:

(-1)^{n} 2^{n-1}

Go to Question:

Prev Question

Next Question