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Answer:
Next three terms are -8, 16 and -32
Step-by-step explanation:
We are given the sequence:-
1, -2, 4, ...
We want to find next three terms:-
1, -2, 4, a4, a5, a6, ...
Since the sequence is geometric because it has common ratio;-
-2/1 = -2
4/-2 = -2
Our common ratio is -2.
General Term of Geometric
[tex] \displaystyle \large{a_n = a_1 {r}^{n - 1} }[/tex]
Our first term or a1 is 1
Our common ratio or r is -2
Therefore:-
[tex] \displaystyle \large{a_n =1 {( - 2)}^{n - 1} }[/tex]
Since we want to find next three terms which are a4,a5 and a6. Substitute n = 4,5 and 6 in.
Finding a4
[tex] \displaystyle \large{a_4 = 1 {( - 2)}^{4 - 1} } \\ \displaystyle \large{a_4 = 1 {( - 2)}^{3 } } \\ \displaystyle \large{a_4 = 1 {( - 8)} } \\ \displaystyle \large{a_4 = - 8}[/tex]
Finding a5
[tex] \displaystyle \large{a_5 = 1 {( - 2)}^{5 - 1} } \\ \displaystyle \large{a_5 = 1 {( - 2)}^{4 } } \\ \displaystyle \large{a_5= 1(16)}\\ \displaystyle \large{a_5 = 16}[/tex]
Finding a6
[tex] \displaystyle \large{a_6= 1 {( - 2)}^{6- 1} } \\ \displaystyle \large{a_6 = 1 {( - 2)}^{5 } } \\ \displaystyle \large{a_6 = 1( - 32)}\\ \displaystyle \large{a_6 = - 32}[/tex]