Write the first five terms of each of the following sequences whose nth terms are:
$ a_{n}=(-1)^{n} \cdot 2^{n} $

Given:

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

To do:

We have to find the first five terms of the given sequence.

Solution:

$a_n=(-1)^{n} \cdot 2^{n}$

Taking $n=1$, we get

$a_1=(-1)^{1} \cdot 2^{1}=(-1)2=-2$

Taking $n=2$, we get

$a_2=(-1)^{2} \cdot 2^{2}=1(4)=4$

Taking $n=3$, we get

$a_3=(-1)^{3} \cdot 2^{3}=(-1)\times8=-8$

Taking $n=4$, we get

$a_4=(-1)^{4} \cdot 2^{4}=1\times16=16$

Taking $n=5$, we get

$a_5=(-1)^{5} \cdot 2^{5}=(-1)\times32=-32$

Hence, the first five terms of the given sequence are $-2, 4, -8, 16$ and $-32$. 

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Updated on: 10-Oct-2022

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