WORKSHEET: Arithmetic Sequence & Series Word Problems, Lecture notes of Calculus

Download WORKSHEET: Arithmetic Sequence & Series Word Problems and more Lecture notes Calculus in PDF only on Docsity! Name______________________________________ Date_______________ Period_________ ARITHMETIC SEQUENCES & SERIES WORKSHEET The general term of an arithmetic sequence is given by the formula an = a1 + (n - 1)d where a1 is the first term in the sequence and d is the common difference. Finding the sum of a given arithmetic sequence: 1. Identify a1, n, and d for the sequence. 2. Find an using an = a1 + (n - 1)d. 3. Substitute and evaluate: 2 )a + a ( n = S n1 n 1. Write down the stated term and the nth term of the following arithmetic sequences a. 7, 11, 15, … (7th) c. 18, 11, 4, … (6th ) b. -7, -5, -3, … (23rd) d. 3, 3 ½, 4, … (16th) 2. Graph Function 1d from above on the graph provided. 3. Find the sum of the following series. (hint: use the formula for arithmetic sequences first to find n) a. 5, 9, 13, …, 101 c. 83, 80, 77, …, 5 b. -17, -12, -7,…, 33 d. 1, 1 ¼ , 1 ½, … 9 ¾ 4. Find the sum of the following series. a. 4, 11, … to 16 terms c. 3, 8 ½, … to 20 terms b. 19, 13, … to 10 terms d. -9, -1, … to 8 terms 5. Fill in the gaps in this arithmetic sequence: -3, ___, ___, ___, ___, ___, 12 6. An arithmetic sequence has a 10th term of 17 and a 14th term of 30. Find the common difference. 7. Find the sum of the first 100 odd numbers 8. Find the sum of the positive terms of the arithmetic sequence 85, 78, 71, … 9. The second term of an arithmetic sequence is 7. The sum of the first 4 terms of the arithmetic sequence is 12. Find the first term a1, and the common difference, d, of the sequence. 10. The first, second, and the nth terms of an arithmetic sequence are 2, 6, and 58 respectively, a. Find the value of n b. For that value of n, find the exact value of the sum of n terms.