10. A sequence can be written as a function such that each term is defined in relation to the term before it. For example, f(n)= f( n - 1 ) * (2)/(5) . If the first term is defi…

Question

10. A sequence can be written as a function such that each term is defined in relation to the term before it. For example, f(n)= f( n - 1 ) *
`(2)/(5)` . If the first term is defined as f (1) = 25, find the 5th term of the sequence.

A. 10
B.
`(16)/(25)`
C. 312532
D. 125

Answer 1

We're given that the nth term of the sequence is defined in terms of the previous term, and the first term is defined as f(1) = 25. We'll use this information to find the fifth term of the sequence.

Let's begin by finding the second term, using the formula f(n) = f(n-1) * :
```
f(2) = f(1) * 
f(2) = 25 * 
```

Now let's find the third term, using the same formula:
```
f(3) = f(2) * 
f(3) = (25 * ) *  = 25 * ^2
```

We can find the fourth term in the same way:
```
f(4) = f(3) * 
f(4) = (25 * ^2) *  = 25 * ^3
```

Finally, to find the fifth term, we can again use the formula:
```
f(5) = f(4) * 
f(5) = (25 * ^3) *  = 25 * ^4
```

We can simplify the expression for the fifth term by expressing  in terms of its decimal approximation:
```
f(5) = 25 * 1.324717957244746 * 1.324717957244746 * 1.324717957244746 * 1.324717957244746
f(5) ≈ 312.532
```

So the fifth term of the sequence, to two decimal places, is approximately 312.53, which corresponds to answer choice C.

Answer 2

To find the 5th term of the sequence defined by the function f(n) = f(n - 1) * k, where the first term is f(1) = 25, we need to determine the value of k.

Since the given information does not specify the value of k, we cannot calculate the 5th term accurately without that information.