Question

If the sixth term in a geometric sequence is 1/625, and the common ratio is 15, find the explicit formula of the sequence.

Answer 1

Answer:

The explicit formula of the sequence is $a_n=5(\frac{1}{5})^{n-1}$ for $n \geq 2$

Step-by-step explanation:

Sixth term in a geometric sequence =$\frac{1}{625}$

Common ratio =$\frac{1}{5}$

Formula of nth term =$a_n=ar^{n-1}$

Substitute the values

So,$\frac{1}{625}=a(\frac{1}{5})^{6-1}\\\frac{1}{625}=a(\frac{1}{5})^{5}\\\frac{1}{625} \times 5^5=a$

5=a

Substitute the value in 1

So,$a_n=5(\frac{1}{5})^{n-1}$

So, Option C is true

Hence the explicit formula of the sequence is $a_n=5(\frac{1}{5})^{n-1}$ for $n \geq 2$