The recursive formula for given sequence is: 
And the terms will be expressed as:

Step-by-step explanation:
First of all, we have to determine if the given sequence is arithmetic sequence or geometric. For that purpose, we calculate the common difference and common ratio
Given sequence is:
11,4,-3,-10,-17...
Here

As the common difference is same, given sequence is an arithmetic sequence.
A recursive formula is a formula that is used to generate the next term of the sequence using the previous term and common difference
So, the recursive formula for an arithmetic sequence is given by:

Hence,
The recursive formula for given sequence is: 
And the terms will be expressed as:

Keywords: arithmetic sequence, common difference
Learn more about arithmetic sequence at:
#LearnwithBrainly
Answer:
32
Step-by-step explanation:
The formula needed to solve this question by hand is:
![x^{\frac{m}{n}} =\sqrt[n]{x^{m}}](https://tex.z-dn.net/?f=x%5E%7B%5Cfrac%7Bm%7D%7Bn%7D%7D%20%3D%5Csqrt%5Bn%5D%7Bx%5E%7Bm%7D%7D)
256^(5/8) = 8th root of 256^5
256^(5/8) = 8th root of 1280
<u>256^(5/8) = 32</u>

Employ a standard trick used in proving the chain rule:

The limit of a product is the product of limits, i.e. we can write

The rightmost limit is an exercise in differentiating

using the definition, which you probably already know is

.
For the leftmost limit, we make a substitution

. Now, if we make a slight change to

by adding a small number

, this propagates a similar small change in

that we'll call

, so that we can set

. Then as

, we see that it's also the case that

(since we fix

). So we can write the remaining limit as

which in turn is the derivative of

, another limit you probably already know how to compute. We'd end up with

, or

.
So we find that