ABCTE Secondary Math Practice Exam

The summation formula for an arithmetic sequence can be represented as Sn = n/2 * (2a1 + (n - 1)d), where Sn is the sum of the first n terms, a1 is the first term of the sequence, n is the number of terms to be summed, and d is the common difference between consecutive terms in the sequence.

This formula works by essentially averaging the first and the last term of the sequence and then multiplying by the number of terms. The term (n - 1)d calculates the total increase from the first term to the nth term due to the common difference, and multiplying 2a1 by n/2 gives a balanced way to account for the contributions of both ends of the sequence. Thus, this formula allows for the calculation of the sum of any arithmetic sequence efficiently.

The other options do not capture the sum of an arithmetic sequence accurately. The second choice, for instance, ignores the sequence's nature of growth and only considers the first term multiplied by n, leading to an incorrect representation of the total. The third option provides a simplified version, which assumes the last term must always be taken into account but does not incorporate the sequence's growth pattern adequately. Lastly, the fourth choice