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A. Finding several terms of a sequence given a general term.

Example 2:
Find the [tex]$5^{\text{th}}$[/tex] to the [tex]$8^{\text{th}}$[/tex] terms of the sequence [tex]$a_n = (-2)^n$[/tex]


Sagot :

To find the 5th to the 8th terms of the sequence given by [tex]\( a_n = (-2)^n \)[/tex]:

1. Identify the Sequence Formula:
The general term of the sequence is [tex]\( a_n = (-2)^n \)[/tex].

2. Calculate the 5th Term:
Substitute [tex]\( n = 5 \)[/tex] into the sequence formula:
[tex]\[ a_5 = (-2)^5 \][/tex]
[tex]\[ a_5 = -32 \][/tex]

3. Calculate the 6th Term:
Substitute [tex]\( n = 6 \)[/tex] into the sequence formula:
[tex]\[ a_6 = (-2)^6 \][/tex]
[tex]\[ a_6 = 64 \][/tex]

4. Calculate the 7th Term:
Substitute [tex]\( n = 7 \)[/tex] into the sequence formula:
[tex]\[ a_7 = (-2)^7 \][/tex]
[tex]\[ a_7 = -128 \][/tex]

5. Calculate the 8th Term:
Substitute [tex]\( n = 8 \)[/tex] into the sequence formula:
[tex]\[ a_8 = (-2)^8 \][/tex]
[tex]\[ a_8 = 256 \][/tex]

Thus, the 5th to the 8th terms of the sequence [tex]\( a_n = (-2)^n \)[/tex] are:
[tex]\[ a_5 = -32, \quad a_6 = 64, \quad a_7 = -128, \quad a_8 = 256 \][/tex]
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