Write down the nth term of the following sequence the following pattern are made using small squares

a) , , b) ,

Step-by-step explanation:

a) The sequence is representative for an arithmetic sequence, whose key characteristic is that difference is between two consecutive elements is the same. In particular, the sequence has a difference of 7 between any two consecutive elements and the initial element is 4. Hence, we can derive the following formula:

, (1)

Where:

- Initial element.

- Difference between two consecutive elements.

- Index.

If we know that and , then the expression for the n-th term of the sequence is:

,

b) In this case, we have a geometric sequence described by the following equation:

,  (2)

The constant element () represents the two extreme squares, whereas the second order binomial represents the total of squares in the middle () and emulates the area formula of the square.

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step-by-step explanation:

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