The nth term of the sequence -1, 2, -4, 8, ... is

Option b: (-1)n 2n-1. Solution: The sequence is -1, 2, -4, 8, ... First term a = -1 , common ratio r = -2 . The nth term is: tn = a × rn-1 = (-1) × (-2)n-1 = (-1) × (-1)n-1 × 2n-1 = (-1)n 2n-1 Hence, Option B is the correct answer.

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

The correct answer is Option b: $(-1)^{n} 2^{n-1}$. The sequence is $-1, 2, -4, 8, \dots$ First term $a = -1$, common ratio $r = -2$. The $n^{\text{th}}$ term is: $$t_n = a \cdot r^{n-1} = (-1) \cdot (-2)^{n-1} = (-1) \cdot (-1)^{n-1} \cdot 2^{n-1} = (-1)^n 2^{n-1}$$ Hence, **Option B** is the correct answer.

Sequence and SeriesMCQMTP May 19 Series IIQuestion 1841 of 212

All Questions

The $\displaystyle n^{th}$ term of the sequence $\displaystyle -1, 2, -4, 8, \dots$ is

Options

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

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

\displaystyle 2^n

DNone of these

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Correct Answer

✅ Option b — $\displaystyle (-1)^{n} 2^{n-1}$

All Options:

A $\displaystyle (-1)^{n-1} 2^{n-1}$
B $\displaystyle (-1)^{n} 2^{n-1}$
C $\displaystyle 2^n$
DNone of these

Detailed Solution & Explanation

The sequence is

\displaystyle -1, 2, -4, 8, \dots

First term

\displaystyle a = -1

, common ratio

\displaystyle r = -2

.
The

\displaystyle n^{\text{th}}

term is:

t_n = a \cdot r^{n-1} = (-1) \cdot (-2)^{n-1} = (-1) \cdot (-1)^{n-1} \cdot 2^{n-1} = (-1)^n 2^{n-1}

Hence, **Option B** is the correct answer.

About This Chapter: Sequence and Series

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Arithmetic & Geometric Progressions

This chapter covers Arithmetic Progressions (AP) and Geometric Progressions (GP). Students learn how to find the nth term, sum of n terms, arithmetic/geometric means, and sum to infinity of a GP.

View Official ICAI Syllabus

Exam Strategy Tip

For complex 'sum of series' questions, a great hack is to substitute n = 1 and n = 2 into the question and the options to see which one matches, completely bypassing the formula.

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The nth\displaystyle n^{th}nth term of the sequence −1,2,−4,8,…\displaystyle -1, 2, -4, 8, \dots−1,2,−4,8,… is