Question

Find the indicated term of the geometric sequence. 5th term of 1, 1 /4,1/16,…

Answer 1

Answer:

$\frac{1}{256}$

Step-by-step explanation:

So generally a geometric sequence can be defined as: $a_n=a_1(r)^{n-1}$ which is the explicit form. The r, is what each previous term is being multiplied by to get the next value which is evident in the recursive form: $a_n = r(a_{n-1})$. Knowing this we can take two values which are "next" to each other to find what r is. In this case I'll just is 1 and 1/4, given these two values we know that: $\frac{1}{4} = 1 * r$, 1*r is just r... so what each term is being multiplied by is 1/4. So let's plug the values into the explicit formula: $a_n=(\frac{1}{4})^{n-1}$ (I didn't put an a_1 value in front, since it's just 1... so it's a bit redundant). Anyways using this formula we simply plug in 5 as n into the equation to find the 5th term: $a_5 = (\frac{1}{4})^{5-1} = (\frac{1}{4})^4 = \frac{1^4}{4^4} = \frac{1}{256}$