Arithmetic Sequences
Arithmetic sequences, a fundamental concept in mathematics, play a pivotal role in various fields, from finance to computer science. These sequences follow a consistent pattern where each term is derived by adding a fixed constant to the preceding term. Understanding arithmetic sequences involves grasping their defining characteristics, such as the common difference between consecutive terms. Mastery of arithmetic sequences enables precise predictions of future terms and facilitates problem-solving in diverse mathematical contexts. Whether analyzing patterns in real-world data or constructing algorithms, proficiency in arithmetic sequences is essential for navigating quantitative landscapes with accuracy and efficiency.
Questions
- How do you find the first four terms given #a_1 = 5#; #a_n = 2a_(n-1) + 4#?
- How do you write the nth term rule for the sequence #11/2,25/6,17/6,3/2,1/6,...#?
- How do you write an equation for the nth term of the arithmetic sequence: -3, -5, -7, -9, ...?
- How do you find a20 for the sequence {2, 2.4, 2.88, 3.456....}?
- How do you write an explicit rule for the sequence 3,5,7,9,...?
- How do you write the next 4 terms in each pattern and write the pattern rule given 460, 435, 410, 385, 360?
- How do you write the first five terms of the arithmetic sequence given #a_1=72, a_(k+1)=a_k-6# and find the common difference and write the nth term of the sequence as a function of n?
- How do you give a recursive formula for the arithmetic sequence where the 4th term is 3; 20th term is 35?
- Is the following sequence arithmetic? If so, identify the common difference. 2.9, 2.7, 2.5, 2.3, . . .
- How do you tell whether the sequence -1,1,3,5,.... is arithmetic, geometric or neither?
- How do you find an equation that describes the sequence #4, 8, 12, 16,...# and find the 13th term?
- What is the general term of an arithmetic sequence with #t_1 = 5# and #t_2 = 2#?
- What is the sum of the arithmetic sequence 3, 9, 15…, if there are 24 terms?
- How do you find the sum of the arithmetic sequence: 2,4,6,8,..., n = 20?
- How do you find the explicit formula for the following sequence 20,15,10,5,0?
- The third term of an arithmetic sequence is 14, and the ninth term is -1. How do you find the first four terms of the sequence?
- How do you find the 12th term of the arithmetic sequence 20, 14, 8, 2, -4, ...?
- How do you write the nth term rule for the sequence #1, 3, 5, 7, 9, ...#?
- The 20th term of an arithmetic series is #log20# and the 32nd term is #log32#. Exactly one term in the sequence is a rational number. What is the rational number?
- How do you find the common difference and the three terms in the sequence given -25, -35, -45, -55,...?