Complete the rule for the arithmetic sequence below. (Hint: An arithmetic sequence is one which goes up or down in equal steps.) Rule: Start at square Add square each time

The sequence provided is . We might note that within this sequence each number increases by the same amount with each step.First thing we need to figure out is the differrence, simply known as 'd'. Difference between two successive numbers in the sequence constitutes 'd'. We can calculate the difference as follows:Take the second term (33) and subtract it from the first term(9). Next, similarily when the third term (57) is subtracted from the second term(33): As such, when calculating 'd' by subtracting every two adjacent terms, we always get 24 - reaffirming an arithmetic series.Now, we want to design an expression that stands for these values in terms of their position. To have a clear thought we could follow a strategy that advises us to eliminate the common difference (24 in this case) and set up remaining as the first term.This suggests that every new term encompasses an addition incurred by more than one 'd'(since at first term 'n=1', however, we began adding at second term‚ where ) As a consequence, we modify the term `n` by subtracting 1, wound up as \((n-1).\):Now, considering represents a component for a given set in a sequence, \( ) as the baseline(first number of sequence) and `n' as the position(number term) brings us to the following yellow-marked sequence:Let's insert ^>\`\`n = 1''(): Let's call ^(2{}''): The position noted as ^(3{}''): Let's put this throughout as ^(4{}''): Considering all this we would infer that the arithmetic series: could be defined by the arithmetic sequence formula: Notably the judgement resonates with the prompted and invited sequence.