Arithmetic and Geometric Series
Name:_____________________________
Per____
Date:___________________________
Determine if the sequences is arithmetic or geometric. Evaluate the related series of each sequence.
1) 13, 15, 17, 19, 21, 23
2) 2, 6, 18, 54, 162
3) 500, 100, 20, 4
4) 22, 28, 34, 40, 46
Determine if the summation is arithmetic or geometric. Evaluate each series described.
5)
6)
7)
8)
9)
10)
*NOTICE, 11-14 gives the type of series. Evaluate the sum of the series up to the nth term.
11) 𝑎1 = 42, 𝑎𝑛 = 146, 𝑛 = 14 *Arithmetic
12) 𝑎1 = 4, 𝑎𝑛 = 22, 𝑛 = 10 *Arithmetic
13) 𝑎1 = 5,
𝑎𝑛 = 160,
𝑛 = 6 *Geometric
14) 𝑎1 = −18,
𝑎𝑛 = −102,
𝑛 = 13 *Arithmetic
15) 20 + 27 + 34 + 41 … , n = 16
16) 2 + 4 + 8 + 16 … , n = 11
17) 7 + 18 + 29 + 40 … , n = 10
18) 7 + 9 + 11 + 13 … , n = 10
Determine the number of terms n in each arithmetic series
19) 𝑎1 = 19,
𝑎𝑛 = 96,
21) 𝑎1 = −3, 𝑑 = 2,
𝑆𝑛 = 690
𝑆𝑛 = 21
20) 𝑎1 = 16,
𝑎𝑛 = 163,
22) 𝑎1 = 4, 𝑑 = 7,
23) (−2) + (−12) + (−22) + (−32) … , 𝑆𝑛 = −224
𝑆𝑛 = 4475
𝑆𝑛 = 229
24) (−16) + (−26) + (−36) + (−46) … , 𝑆𝑛 = −1818
Determine the number of term n in each geometric seris
25) 𝑎1 = 10
𝑎𝑛 = 810
𝑆𝑛 = 1210
26) 𝑎1 = 8
𝑟 = 11
𝑆𝑛 = 1064