How do you write a rule for the nth term of the geometric term given the two terms $a_{2} = 2, a_{5} = \frac{1}{4}$ $a_2=2, a_5=1/4$ ?

Question

How do you write a rule for the nth term of the geometric term given the two terms $a_{2} = 2, a_{5} = \frac{1}{4}$ $a_2=2, a_5=1/4$ ?

1 Answer

Impact of this question

4259 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-22T01:38:32

$a_{n} = 4 \cdot {(\frac{1}{2})}^{n - 1}$ $a_n=4*(1/2)^(n-1)$

Explanation:

The general form for a geometric sequence is:
$a_{n} = a_{1} \cdot r^{n - 1}$ $a_n=a_1*r^(n-1)$

With this, you can write a system of equations:
$a_{2} = a_{1} \cdot r^{2 - 1}$ $a_2=a_1*r^(2-1)$
$a_{5} = a_{1} \cdot r^{5 - 1}$ $a_5=a_1*r^(5-1)$

$2 = a_{1} \cdot r^{1}$ $2=a_1*r^1$
$0.25 = a_{1} \cdot r^{4}$ $0.25=a_1*r^4$
$\frac{r^{4}}{r^{1}} = \frac{0.25}{2}$ $r^4/r^1=0.25/2$
$r^{3} = 0.125$ $r^3=0.125$
$r = 0.5$ $r=0.5$

Now, find the first term.
$a_{2} = a_{1} \cdot {0.5}^{1}$ $a_2=a_1*0.5^1$
$2 = a_{1} \cdot 0.5$ $2=a_1*0.5$
$a_{1} = 4$ $a_1=4$

Using the formula stated above, we get:
$a_{n} = 4 \cdot {0.5}^{n - 1}$ $a_n=4*0.5^(n-1)$

Science

Math

Humanities

... and beyond

How do you write a rule for the nth term of the geometric term given the two terms $a_{2} = 2, a_{5} = \frac{1}{4}$ $a_2=2, a_5=1/4$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you write a rule for the nth term of the geometric term given the two terms a_2=2, a_5=1/4a2=2,a5=14a_2=2, a_5=1/4?

1 Answer

Explanation:

Related questions

Impact of this question

How do you write a rule for the nth term of the geometric term given the two terms $a_{2} = 2, a_{5} = \frac{1}{4}$ $a_2=2, a_5=1/4$ ?