CBSE BoardEnglish MediumSTD 10MathsArithmetic Progressions3 Marks
Question
Write the first five terms of the following sequences whose $n^{th}$ terms are:
$a^n = (-1)^n 2^n.$
✓
Answer
$a^n = (-1)^n 2^n.$
Here, the $n^{th}$ term is given by the above expression. So, to find the first term we use $n = 1$, we get,
$a_1 = (-1)^1.2^1$
$= (-1).2$
$= -2$
Similarly, we find the other four terms,
Second term $(n = 2),$
$a_2 = (-1)^2.2^2$
$= 1.4$
$= 4$
Third term $(n = 3),$
$a_3 = (-1)^3.2^3$
$= (-1).8$
$= -8$
Fourth term $(n = 4),$
$a_4 = (-1)^4.2^4$
$= 1.16$
$= 16$
Fifth term $(n = 5),$
$a_5 = (-1)^5.2^5$
$= (-1).32$
$= -32$
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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