find the 75th term of the arithmetic sequence 3,7,11,15,19,...​

Answer:The final answer is: $\boxed{299}$Step-by-step explanation:## Step 1: Identify the common difference of the arithmetic sequenceThe common difference (d) is the difference between any two consecutive terms. Let's calculate d: d = 7 - 3 = 4, d = 11 - 7 = 4, d = 15 - 11 = 4. The common difference is 4.## Step 2: Use the formula for the nth term of an arithmetic sequenceThe formula for the nth term is: $a_n = a_1 + (n-1)d$, where $a_n$ is the nth term, $a_1$ is the first term, n is the term number, and d is the common difference. Given $a_1 = 3$, d = 4, and n = 75, we can plug these values into the formula.## Step 3: Calculate the 75th term$a_{75} = 3 + (75-1) \times 4$$a_{75} = 3 + 74 \times 4$$a_{75} = 3 + 296$$a_{75} = 299$

Answered by elmagaan24 | 2025-08-03