1. Let's start with a simple problem: Find the 5th term of the arithmetic sequence where the first term $a_1=3$ and the common difference $d=4$. 2. The formula for the $n$th term of an arithmetic sequence is: $$a_n = a_1 + (n-1)d$$ This means you start with the first term and add the common difference multiplied by one less than the term number. 3. Substitute the values into the formula: $$a_5 = 3 + (5-1) \times 4$$ 4. Simplify inside the parentheses: $$a_5 = 3 + 4 \times 4$$ 5. Multiply: $$a_5 = 3 + 16$$ 6. Add to find the 5th term: $$a_5 = 19$$ 7. So, the 5th term of the sequence is 19. --- 1. Now, let's find the sum of the first 6 terms of the same arithmetic sequence. 2. The formula for the sum of the first $n$ terms of an arithmetic sequence is: $$S_n = \frac{n}{2} (2a_1 + (n-1)d)$$ 3. Substitute $n=6$, $a_1=3$, and $d=4$: $$S_6 = \frac{6}{2} (2 \times 3 + (6-1) \times 4)$$ 4. Simplify inside the parentheses: $$S_6 = 3 (6 + 5 \times 4)$$ 5. Multiply: $$S_6 = 3 (6 + 20)$$ 6. Add inside the parentheses: $$S_6 = 3 \times 26$$ 7. Multiply to find the sum: $$S_6 = 78$$ 8. Therefore, the sum of the first 6 terms is 78.