Geometric Progression Explicit

Algebra Level 2

If $4, x, y, 108, \dots$ forms a geometric progression, which of the following represents an explicit formula for the progression?

A_n = 3 \cdot 4^{n}

A_n = 3 \cdot 4^{n-1}

A_n = 4 \cdot 3^{n}

A_n = 4 \cdot 3^{n-1}

2 solutions

Parth Sankhe
Oct 18, 2018

Writing $y^2= x × 108$ and $x^2=4×y$ , we get x = 12 and y= 36.

Thus, the general expression becomes $4 \cdot 3^{n-1}$ ; putting n = 1 will give you the first term, 4.

Blan Morrison
Oct 18, 2018

Given that the first term is 4, we can use the process of elimination to get the correct answer.

The answer cannot be A or C, because $3\cdot 4^n$ , where $n$ is an integer, cannot be 4. Since 4 is the 1st term, that means $n=1$ . However, $4\cdot 3^1\not=4$ , so the answer is D, or $A_n=4\cdot 3^{n-1}$ . $~\beta_{\lceil \mid \rceil}$

Geometric Progression Explicit

2 solutions

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