If the sum of the first n terms of an arithmetic series is given by S_n = 5n^2 + 3n, what is the 5th term?
Practice Questions
1 question
Q1
If the sum of the first n terms of an arithmetic series is given by S_n = 5n^2 + 3n, what is the 5th term?
38
43
48
53
The 5th term can be found using a_n = S_n - S_(n-1). Calculate S_5 and S_4, then find a_5 = S_5 - S_4 = (5(5^2) + 3(5)) - (5(4^2) + 3(4)) = 38.
Questions & Step-by-step Solutions
1 item
Q
Q: If the sum of the first n terms of an arithmetic series is given by S_n = 5n^2 + 3n, what is the 5th term?
Solution: The 5th term can be found using a_n = S_n - S_(n-1). Calculate S_5 and S_4, then find a_5 = S_5 - S_4 = (5(5^2) + 3(5)) - (5(4^2) + 3(4)) = 38.
Steps: 10
Step 1: Understand that S_n represents the sum of the first n terms of the arithmetic series.
Step 2: Write down the formula for S_n, which is S_n = 5n^2 + 3n.
Step 3: To find the 5th term (a_5), we need to calculate S_5 and S_4.
Step 4: Calculate S_5 by substituting n = 5 into the formula: S_5 = 5(5^2) + 3(5).
