Write the first five terms of the following sequences whose n^ th… - Vidyadip

Question

Write the first five terms of the following sequences whose $n^{th}$ terms are:
$a^n=(-1)^n 2^n$

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Answer

$a^n=(-1)^n 2^n$
Here, the $\mathrm{n}^{\text {th }}$ term is given by the above expression. So, to find the first term we use $\mathrm{n}=1$, we get,
$ a_1=(-1)^1 \cdot 2^1 $
$ =(-1) \cdot 2 $
$ =-2$
Similarly, we find the other four terms,
$ \text { Second term }(n=2), $
$ a_2=(-1)^2 \cdot 2^2 $
$ =1.4 $
$ =4 $
$ \text { Third term }(n=3) $
$ a_3=(-1)^3 \cdot 2^3 $
$ =(-1) \cdot 8 $
$ =-8$
Fourth term $(n=4)$,
$ a_4=(-1)^4 \cdot 2^4 $
$ =1.16 $
$ =16$
Fifth term $(\mathrm{n}=5)$,
$ a_5=(-1)^5 \cdot 2^5 $
$ =(-1) \cdot 32 $
$ =-32$
Therefore, the first five terms of the given A.P are $a_1=-2, a_2=4, a_3=-8, a_4=16, a_5=-32$.

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