Some sequences follow predictable patterns though the pattern

Some sequences follow predictable patterns, though the pattern might not be immediately apparent. Other sequences have no pattern at all. Explain, when possible, patterns in the following sequences: a. 5, 4, 3, 2, 1 b. 3, 5, 1, 2, 4 c. 2, 4, 3, 5, 1, 7 d. S, M, T, W, T, F, S e. 31, 28, 31, 30, 31 f. 1, 2, 3, 4, 5, . . . , 999, 1000 g. 1, -1, . . . h. 4, 7, 10, 13, 16, . . . i. 10, 1000, 100000, . . .

Sequences and Series Keeper Honors Algebra II

A sequence is a function, where the domain is a set of consecutive positive integers beginning with 1. An infinite sequence is a function having for its domain the set of positive integers, {1, 2, 3, 4, 5, …}. A finite sequence is a function having for its domain a set of positive integers, {1, 2, 3, 4, 5, …, n}, for some positive integer n.

In a formula, the function values are known as terms of the sequence. • The first term in a sequence is denoted as a 1, • the fifth term as a 5 , • and the nth term, or the general term, as an.

For the sequence 1, 3, 5, 7, 9, 11, 13, … find each of the following: a) S 1 b) S 5 c) S 7

Find and evaluate the sum.

A sequence may be defined recursively or by using a recursion formula. Such a definition lists the first term, or the first few terms, and then describes how to determine the remaining terms from the given terms.

Jim’s bank account had an initial deposit of $380, earning 3. 5% interest per year compounded annually. a. Find the balance each year for the first 5 years. a. Write a recursive formula and an explicit formula defining his account balance. a. For very large values of n, which formula gives a more accurate balance? Explain

Suppose that when a plant first starts to grow, the stem has to grow for two months before it is strong enough to support branches. At the end of the second month, it sprouts a new branch and will continue to sprout one new branch each month. The new branches also each grow for two months and then start to sprout one new branch each month. If this pattern continues, how many branches will the plant have after 10 months?