Section 8.1: Arithmetic Sequences

This section introduces arithmetic sequences, their formulas, and methods to find terms and sums of sequences.

Example 1: Finding a Term in an Arithmetic Sequence

Given the sequence 3, 7, 11, … find the 10th term.

Step 1: Determine common difference: d = 7 - 3 = 4

Step 2: Use formula \( a_n = a_1 + (n-1)d \)

Step 3: \( a_{10} = 3 + (10-1)*4 = 3 + 36 = 39 \)

Example 2: Sum of an Arithmetic Sequence

Find the sum of the first 15 terms of 2, 5, 8, …

Step 1: First term \( a_1 = 2 \), common difference \( d = 3 \)

Step 2: Last term \( a_{15} = a_1 + (n-1)d = 2 + 14*3 = 44 \)

Step 3: Sum formula \( S_n = \frac{n}{2} (a_1 + a_n) = \frac{15}{2}(2+44) = 345 \)

Practice Problems

  1. Find the 12th term of the sequence 5, 9, 13, …
  2. Sum the first 20 terms of 1, 4, 7, …
  3. Given \( a_1 = 8 \) and \( d = 5 \), find \( a_{15} \)
  4. Sum the first 25 terms of 2, 6, 10, …
  5. Find the 30th term if the 5th term is 12 and the 8th term is 21
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