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}}`Step-by-step 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((1)/(2))^{n\text{ -1}}`

thus, if n= 9, we get:

`a_9=6\cdot((1)/(2))^{9\text{ -1}}`

that is:

`a_9=6\cdot((1)/(2))^8`

this is equivalent to:

`a_9=(6)/(2^8)=(6)/(256)=(3)/(128)`

we can conclude that the correct answer is:

Answer:

The 9th term is:

`(3)/(128)`