Answer:
Step-by-step explanation:
Let us consider the equation
For a quadratic equation in a standard form, , the axis of symmetry is the vertical line
.
Here in this case we have,
Putting the values we get,
We can see that the axis of symmetry is x=3 and the graph is giving minimum at x=3.
Therefore, the required equation is . Refer the image attached.
Given:
The different recursive formulae.
To find:
The explicit formulae for the given recursive formulae.
Solution:
The recursive formula of an arithmetic sequence is and the explicit formula is
, where a is the first term and d is the common difference.
The recursive formula of a geometric sequence is and the explicit formula is
, where a is the first term and r is the common ratio.
The first recursive formula is:
for
.
It is the recursive formula of an arithmetic sequence with first term 5 and common difference 5. So, the explicit formula for this recursive formula is:
Therefore, the correct option is A, i.e., .
The second recursive formula is:
for
.
It is the recursive formula of a geometric sequence with first term 5 and common ratio 3. So, the explicit formula for this recursive formula is:
Therefore, the correct option is F, i.e., .
The third recursive formula is:
for
.
It is the recursive formula of an arithmetic sequence with first term 5 and common difference 3. So, the explicit formula for this recursive formula is:
Therefore, the correct option is D, i.e., .