Question

Find an equation for the nth term in the following sequence: 2, 8, 32, 128, 512...

Answer 1

Answer:

$a_n = 2(4) ^{n-1}$

Step-by-step explanation:

The sequence shown matches that of a geometric sequence of radius 4. To prove it, divide the term $\frac{a_{n + 1}}{a_n}$ and check that $\frac{a_{n + 1}}{a_n}=4$

Then the formula that represents this sequence is:

$a_n = a_1(r)^{n-1}$

Where $a_1$ is the first term of the series = 2 and $r$ is the radius of convergence = 4.

Then the equation is:

$a_n = 2(4) ^{n-1}$

Answer 2

Answer:

nth term of the sequence is $2^{2n-1}$ or $T_{n}=2.(4)^{n-1}$

Step-by-step explanation:

The given sequence is 2, 8, 32, 128, 512.........

Or we can rewrite the sequence as $2, 2^{3}, 2^{5},2^{7},2^{9} ,...............nth term.$

Now the new form of sequence confirms that the sequence is an exponential sequence.

Therefore nth term of the sequence will be $T_{n}=2^{2n-1}$ Or $T_{n}=2.(4)^{n-1}$