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]
