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Suppose a term of a geometric sequence is a4 = 121.5 and the common ratio is 3. Write the formula for this sequence in the form an = a1 ⋅ rn−1. Explain how you arrived at your answer.

Sagot :

MrRoyal

Answer:

[tex]a_n = 4.5 * 3^{n-1}[/tex]

Step-by-step explanation:

Given

[tex]a_4 = 121.5[/tex]

[tex]r = 3[/tex]

Required

[tex]a_n = a_1 * r^{n -1}[/tex]

Substitute 4 for n in [tex]a_n = a_1 * r^{n -1}[/tex]

[tex]a_4 = a_1 * r^{4 -1}[/tex]

[tex]a_4 = a_1 * r^3[/tex]

Substitute 121.5 for [tex]a_4[/tex]

[tex]121.5 = a_1 * 3^3[/tex]

[tex]121.5 = a_1 * 27[/tex]

Solve for a1

[tex]a_1 = \frac{121.5}{27}[/tex]

[tex]a_1 = 4.5[/tex]

So, we have:

[tex]a_n = a_1 * r^{n -1}[/tex]

[tex]a_n = 4.5 * 3^{n-1}[/tex]

freazefire0

Answer:

First I substituted 121.5 for an, 4 for n, and 3 for r in the general form. Then I solved to find a1 = 4.5. Finally, I substituted 4.5 for a1 and 3 for r in the general form to get an = 4.5 ⋅ 3n−1.

Step-by-step explanation:

sample answer on edge ;)

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