Find the 12th term of the geometric sequence
2
,
−
8
,
32
,
.
.
.
2,−8,32,...

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:

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;

Hence the 12th term of the geometric sequence is -8,388,608

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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

So,

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:

now, put the values of a and r:

a12 = 2 * (-4,194,304)

a12 = -8,388,608

Hence, the 12th term of the geometric sequence would be -8,388,608.