find the sum of the arithmetic series 3 7 11 15
Answer (1)
Step-by-step explanation:Identify the details of the arithmetic series:The series is: 3, 7, 11, 15First term ( a_1 = 3 )Common difference ( d = 7 - 3 = 4 )Number of terms ( n = 4 )The sum of the first ( n ) terms of an arithmetic series is given by:[ S_n = \frac{n}{2} (2a_1 + (n-1)d) ]Plugging in the values:[ S_4 = \frac{4}{2} (2 \times 3 + (4-1) \times 4) \ = 2 (6 + 3 \times 4) \ = 2 (6 + 12) \ = 2 \times 18 = 36 ]Answer: The sum of the arithmetic series is 36.
