Question

Which sequence is geometric and has 1/4 as its fifth term and 1/2 as the common ratio?

Answer 1

5th term = a1r^4   where a1 = first term and r = common ratio

so 1/4 = a1 * (1/2)^4

a1 = 1/4 / (1/2)^4  =  4

so the sequence  is  4 , 4*1/2, 4*(1/2)^2...

= 4, 2, 1, 1/2, 1/4 .....

Answer 2

Answer:

4, 2, 1, $\frac{1}{2}$.......

Step-by-step explanation:

Since explicit formula of a geometric sequence is represented by An = $A_{1}(r)^{n-1}$

It is given in the question that fifth term of the sequence is $(\frac{1}{4})$ and common ratio of the sequence is $\frac{1}{2}$.

Now from the explicit formula

$A_{5}=\frac{1}{4} =A_{1}(\frac{1}{2})^{5-1}$

$\frac{1}{4}=A_{1}( \frac{1}{2})^{4}$

$A_{1} \frac{2^{4} }{4}$

$\frac{16}{4}$ = 4

Therefore, sequence will be 4, 4 × $(\frac{1}{2})$, 4 × $\frac{1}{2}^{2}$, 4 × $(\frac{1}{2})$³.........

= 4, 2, 1, $\frac{1}{2}$.......