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Arithmetic Sequences & Series Word Problems: A Comprehensive Guide, Lecture notes of Calculus

Holy Angel University (HAU)Calculus

ARITHMETIC SEQUENCES & SERIES WORKSHEET. The general term of an arithmetic sequence is given by the ... Finding the sum of a given arithmetic sequence:.

Typology: Lecture notes

2021/2022

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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
=
Sn1
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
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Name______________________________________ Date_______________ Period_________

ARITHMETIC SEQUENCES & SERIES WORKSHEET

The general term of an arithmetic sequence is given by the formula an = a 1 + (n - 1)d where a 1 is the first term in the sequence and d is the common difference. Finding the sum of a given arithmetic sequence:

  1. Identify a 1 , n, and d for the sequence.
  2. Find an using an = a 1 + (n - 1)d.
  3. Substitute and evaluate:

n(a+a )

S n=^1 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)

  1. Graph Function 1d from above on the graph provided.
  2. 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

  1. 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

  1. Fill in the gaps in this arithmetic sequence: -3, ___, ___, ___, ___, ___, 12
  2. An arithmetic sequence has a 10th^ term of 17 and a 14th^ term of 30. Find the common difference.
  3. Find the sum of the first 100 odd numbers
  4. Find the sum of the positive terms of the arithmetic sequence 85, 78, 71, …
  5. 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 a 1 , and the common difference, d, of the sequence.

  1. 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.

  1. Sonia has 55 blocks. She decides to stack up all the blocks so that each row has one less block than the row below. She wants to end up with just 1 block on top. How many should she put in the bottom row?
  2. A theater has 32 rows of seats. If there are 26 seats in the 1st row, 30 in the 2nd, 34 in the 3rd, and so on, how many seats are there in all?
  3. A tube well is bored 800 meters deep. The 1st^ meter costs $250 and the cost per meter increases by $50 for every subsequent meter. Find the cost of boring the 750th^ meter and the total cost incurred for the entire job.
  4. Derive the sum of the arithmetic series.