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