ExplanationThis is an arithmetic sequence: each new number is created by adding 5 to the previous number in the sequence.
Calculate the first few terms of the sequence: 1, 6, 11, 16, 21, and so on.
Arithmetic sequences can be written in this form: \(a_n = a_1 + k(n - 1)\), where k is the added constant and n is the number of the desired term. In this case, the function is: \(a_n = 1 + 5(n - 1)\).
The 75th term of this sequence is \(a_{75} = 1 + 5(74) = 371\).
To find the sum of an arithmetic sequence, multiply the average value of the terms by the number of terms.
The average of any evenly spaced set is equal to the midpoint between the first and last terms.
The average of the 1st and 75th terms is \(\frac{1+371}{2}= 186\). There are 75 terms. Therefore, the sum of the first 75 terms \(= 186 \times 75 = 13,950\).
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