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

If the sum of the first n terms of an arithmetic series is given by S_n = 5n + 3, what is the 10th term? (2023)

If the sum of the first n terms of an arithmetic series is given by S_n = 5n + 3, what is the 10th term? (2023)

Step 1: Understand that S_n represents the sum of the first n terms of the arithmetic series.
Step 2: The formula for S_n is given as S_n = 5n + 3.
Step 3: To find the 10th term (T_10), we need to calculate S_10 and S_9.
Step 4: Calculate S_10 by substituting n = 10 into the formula: S_10 = 5(10) + 3.
Step 5: Perform the calculation: S_10 = 50 + 3 = 53.
Step 6: Now calculate S_9 by substituting n = 9 into the formula: S_9 = 5(9) + 3.
Step 7: Perform the calculation: S_9 = 45 + 3 = 48.
Step 8: Use the formula T_n = S_n - S_(n-1) to find T_10: T_10 = S_10 - S_9.
Step 9: Substitute the values: T_10 = 53 - 48.
Step 10: Perform the subtraction: T_10 = 5.

Arithmetic Series – Understanding the properties of arithmetic series, including the formula for the sum of the first n terms and how to derive individual terms from it.
Sum of Terms – Using the formula for the sum of terms to find specific terms in a sequence.
Difference of Sums – Applying the relationship between the sum of terms to find the nth term by subtracting the sum of the previous terms.