f8M9X_SequencesAndSeries * @ @ S + Share T File Edit View Insert Format Tools Add-ons Help 100% Normal text Arial 11 + ... 31 1 1 13 1 1 1 1 1 1 1 15 1 1 1 1 . C PROBLEM #1 Identify each of the following sequences as finite or infinite. Then classify as arithmetic, geometric, or neither. Finally find an explicit formula (rule for the nth term) for each. Designate the first term with n = 1. Table 1 Example: Infinite 5, 40, 320, 2560, 20480, ... Geometric + Formula: #7 = 5(8) #-1 a. 4, 8, 12, 16, 20, 24, ... b. 2b, 4b, 6b, 8b, 10b, 12b, 14b c. 3, -9, 27, -81, .. 1 3 9 27 729 d. 2'2 2 2 "2 e. 1, 4, 9, 16, 25, 36, ... Consider some of the same sequences written as series. Examples: 1 + 4 + 9 + 16 + 25 + 36 + ... 5 + 40 + 320 + 2560 + 20480 + ... Because situations often arise where a large list of numbers needs to be summed, mathematicians have a shorthand notation that uses the Greek letter sigma. 3 stopping point +f8M9X_SequencesAndSeries * @ @ + Share File Edit View Insert Format Tools Add-ons Help 100% Normal text Arial 11 + 31 1 2 1 1 13 1 1 1 |1 1 14 1 151 1 1|1 1 1 index of summation starting point Note: it is important to realize that some series can be represented with sigma notation that uses an index variable other than n or have a different integer starting value. For example: C Can + 1= [2j+3 = >2i-3=3+5+7+9+11 PROBLEM #2 Write the expanded series represented by the given summation notation. 212 + a. (41 -3) b. C. PROBLEM #3 Express the series below in summation notation for the specified number of terms. a. 2 +4+8 + 16 b. 10 + 14 + 18 + 22 12 3 4 5 C. 27345 6 3 PROBLEM #4 +