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The first term of a geometric sequence is −2 and the common ratio is 3. What is the fourth term of the sequence?

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Luv2Teach

Answer:

Step-by-step explanation:

The formula for a geometric sequence is

[tex]a_n=a_1*r^{n-1}[/tex] where n is the position in the sequence, a1 is the first number in the sequence, and r is the common ratio. For us, a1 = -2 and r = 3, n = the 4th term:

[tex]a_4=-2*3^{4-1}[/tex] and

[tex]a_4=-2*3^3[/tex] and

[tex]a_4=-2*27[/tex] so

[tex]a_4=-54[/tex]

The 4th term in the geometric sequence is -54.