Question

1Find the 9th term of the geometric sequence whose common ratio is 1/2and whose first term is 6.

Answer 1

General category: Sequences, Series, and Mathematical Induction

Sub-category: Formulas and Notation for Sequences and Series

Topic: Recursive Formulas and explicit Formulas.

Introduction:

Given a geometric sequence with the first term a_1 and the common ratio r, the nth term is given by the following formula:

$a_n=a_1\cdot r^{n\text{ -1}}$Explanation:

If we have a geometric sequence whose common ratio is 1/2 and whose first term is 6, then the nth term is given by the following formula:

$a_n=6\cdot(\frac{1}{2})^{n\text{ -1}}$

thus, if n= 9, we get:

$a_9=6\cdot(\frac{1}{2})^{9\text{ -1}}$

that is:

$a_9=6\cdot(\frac{1}{2})^8$

this is equivalent to:

$a_9=\frac{6}{2^8}=\frac{6}{256}=\frac{3}{128}$

we can conclude that the correct answer is:

Answer:

The 9th term is:

$\frac{3}{128}$