If the sum of the first n terms of an arithmetic series is given by S_n = 5n + 3

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Question: If the sum of the first n terms of an arithmetic series is given by S_n = 5n + 3, what is the 4th term? (2023)

Options:

Correct Answer: 23

Exam Year: 2023

Solution:

The 4th term can be found using T_n = S_n - S_(n-1). Here, S_4 = 5(4) + 3 = 23 and S_3 = 5(3) + 3 = 18. Thus, T_4 = 23 - 18 = 5.

If the sum of the first n terms of an arithmetic series is given by S_n = 5n + 3, what is the 4th term? (2023)

If the sum of the first n terms of an arithmetic series is given by S_n = 5n + 3, what is the 4th term? (2023)

Step 1: Understand that S_n represents the sum of the first n terms of the arithmetic series.
Step 2: Use the formula for S_n given in the question: S_n = 5n + 3.
Step 3: To find the 4th term (T_4), we need to calculate S_4 and S_3.
Step 4: Calculate S_4 by substituting n = 4 into the formula: S_4 = 5(4) + 3 = 20 + 3 = 23.
Step 5: Calculate S_3 by substituting n = 3 into the formula: S_3 = 5(3) + 3 = 15 + 3 = 18.
Step 6: Now, use the relationship T_n = S_n - S_(n-1) to find T_4: T_4 = S_4 - S_3.
Step 7: Substitute the values: T_4 = 23 - 18 = 5.
Step 8: Conclude that the 4th term of the series is 5.

Arithmetic Series – Understanding the properties of arithmetic series, including the formula for the sum of the first n terms.
Finding Terms from Sums – Using the relationship between the sum of terms and individual terms to find specific terms in a series.