What conclusions can you draw about the relationship between arithmetic or geometric sequences and linear or exponential functions? practice answer in complete sentences.

→→Arithmetic sequence: When we talk about arithmetic sequence . there is a thing called Common Difference , which can be calculated by finding the difference between two consecutive terms, that is the beginning term and it's Succeeding term.

→n th term of Arithmetic sequence= A + (n-1) d, Here A= First term, d=Common Difference

If value of n changes ,that is for different positive integral values of n, we get different terms in a sequence.

→→→If we compare it with , linear function, which is represented as

→y= m x + c, here m= Slope of line, C= Y intercept

So, if slope of line changes , we get different equation of line.

→→When we talk about geometric sequence, the word comes into notion is Common ratio, which can be calculated by dividing the succeeding term by preceding term.  

→→General formula for Geometric Sequence = , where a = First term , r= Common ratio

For, r> 1, each succeeding term increases by a fixed value called common ratio, and when r<1, each succeeding term is less than by it previous term by a fixed quantity, called common ratio.

→→Similarly, exponential function behaves in same way.

General formula for exponential functions  = , or   where a = Starting  term

Keeping the value of b and ,a fixed, if n is positive , graph of the function is Strictly increasing,and if n is negative graph of function is strictly decreasing.

Relationship between:      

Arithmetic or geometric sequences and Linear or exponential function

If you look the graph of the arithmetic sequence, they are always linear

and the graph of the geometric sequence are always exponential.

25/4

step-by-step explanation:

call segment cd's length x. because dc and ab are parallel, angle acd and cab, so triangles adc and abc are similar and we can set up the equation x / ac = ac / ab, or x / 5 = 5 / 4 and x = 25/4.

i think the correct option is the second option.