The 12th term of the geometric sequence would be -8,388,608.
Step-by-step explanation:
Given that,
The first term of geometric sequence is = a1 = 2
a2 = -8
a3 = 32
Now, the formula for nth term of a geometric sequence is [tex]an = a*r^{n-1}[/tex]
So,
[tex]a1 = a*r^{1-1} = a*rx^{0} = a*1 = a[/tex]
[tex]a2 = a*r^{2-1} = a*rx^{1} = a*r[/tex]
Now,
a = 2
a*r = -8
By putting the value of a, we get
2*r = -8
or
r = -4
For 12th term, the formula would be:
[tex]a1 2 = a*r^{12-1} = a*r^{11}[/tex]
now, put the values of a and r:
[tex]a12 = 2*(-4)^{11}[/tex]
a12 = 2 * (-4,194,304)
a12 = -8,388,608
Hence, the 12th term of the geometric sequence would be -8,388,608.
The 12th term of the geometric sequence is -8,388,608
The formula for calculating the nth term of a geometric sequence is expressed as:
[tex]T_n = ar^{n-1}[/tex]
a is the first term
n is the number of terms
r is the common ratio
Given the sequence of numbers 2, -8, 32...
a = 2
r = -8/2 = 32/-8 =-4
n = 12 (We need the 12th term)
Substitute the given parameters into the formula;
[tex]T_{12} = 2(-4)^{12-1}\\T_{12}=2(-4)^{11}\\T_{12}=2(-4,194,304)\\T_{12}=-8,388,608\\[/tex]
Hence the 12th term of the geometric sequence is -8,388,608
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