A sequence is a list of numbers written in a definite order: Each number is called a ..., an a1, A2, A3, A4, called the a) an = For each of the following sequences, tell whether they converge or diverge as n → ∞o n b) bn = 1 - 2n 2n c) bn 3n+4 (11.2) The successor to an is represented by A sequence can be considered a function whose domain is d) an = sin n (-1)" 3+5 100 n! and an is e) an = f) tn A series is the sum of the terms of a sequence. To indicate the sum, we use sigma E notation. Write the following infinite sum in 2 notation: 1+3+9+27+81 +... What is the formula for the sum of an infinite geometric series? Under what conditions is this sum finite?

Question 13 .... is define by A sequence a0, a1, a2, a3,.. an = 7an-1 – 10an-2, for n > 2 and a=5 and a =16. An, Prove that an = 3 x 2" + 2 x 5" for all integers n > 0. Edit View Insert Format Tools Table

Let b1, b2, b3,... be the sequence of numbers defined by b1 = 1, and b, V6 + bn-1 if n > 2. Prove that 0 1.

A sequence ai, a2, a3, . . . is defined by An+1 4а, — 3, п > 1 - a1 = k, where k is a positive integer. Given that E ar = 66, find the value of k.