How does an arithmetic sequence work

Given the arithmetic sequence, find a formula for the general term and use it to determine the th term. Find the 50 th positive odd integer. Find the 50 th positive even integer.

Find the 40 th term in the sequence that consists of every other positive odd integer: 1, 5, 9, 13,…. Find the 40 th term in the sequence that consists of every other positive even integer: 2, 6, 10, 14,…. Given the terms of an arithmetic sequence, find a formula for the general term. Find all arithmetic means between the given terms. Calculate the indicated sum given the formula for the general term.

Find the following. The sum of the first k positive odd integers. The sum of the first k positive even integers. The first row of seating in a small theater consists of 8 seats.

Each row thereafter consists of 3 more seats than the previous row. If there are 12 rows, how many total seats are in the theater? The first row of seating in an outdoor amphitheater contains 42 seats, the second row contains 44 seats, the third row contains 46 seats, and so on.

If there are 22 rows, what is the total seating capacity of the theater? If a triangular stack of bricks has 37 bricks on the bottom row, 34 bricks on the second row and so on with one brick on top. How many bricks are in the stack? Each successive row of a triangular stack of bricks has one less brick until there is only one brick on top. How many rows does the stack have if there are total bricks? Determine the total salary obligation over the 10 year period.

A clock tower strikes its bell the number of times indicated by the hour. How many times does the clock tower strike its bell in a day? Is the Fibonacci sequence an arithmetic sequence? Under what circumstances would this formula be useful? Explain using an example of your own making. Discuss methods for calculating sums where the index does not start at 1.

A famous story involves Carl Friedrich Gauss misbehaving at school. As punishment, his teacher assigned him the task of adding the first integers. The legend is that young Gauss answered correctly within seconds. What is the answer and how do you think he was able to find the sum so quickly? Varsity Tutors connects learners with experts.

Instructors are independent contractors who tailor their services to each client, using their own style, methods and materials. Arithmetic Sequences An arithmetic sequence is a sequence of numbers which increases or decreases by a constant amount each term. Note that since the sequence is decreasing, the common difference is negative.

Subjects Near Me. Download our free learning tools apps and test prep books. In other words, we just add the same value each time Example: 1, 4, 7, 10, 13, 16, 19, 22, 25, Example: continued 1, 4, 7, 10, 13, 16, 19, 22, 25, Example: Write a rule, and calculate the 9th term, for this Arithmetic Sequence: 3, 8, 13, 18, 23, 28, 33, 38, Arithmetic Sequences are sometimes called Arithmetic Progressions A.