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Find the first five terms of the sequence with an = 5 - 2n. Enter them in order (a1, a2, a3, a4, a5). Find the?

• Find the first five terms of the sequence with an = 5 - 2n. Enter them in order (a1, a2, a3, a4, a5). Find the geometric mean of 1/8 and 1/18. Find the first five terms of the sequence with a1 = 9 and an = 2an-1 - 3. Enter them in order (a1, a2, a3, a4, a5). Find the sum S27 for the geometric series: -7 + 14 - 28 + 56... Find the first three terms of the geometric sequence with a6 = 128 and a11

• Answer:

  1). Find the first five terms of the sequence with an = 5 - 2n. Enter them in order (a1, a2, a3, a4, a5). 3, 1, -1, -3, -5, ... 2). Find the geometric mean of 1/8 and 1/18. On a calculator, you would multiply the numbers together, press equal, then the exponent key and then enter 0.25 on the last part). The geometric mean = 0.019641855... 3). Find the first five terms of the sequence with a1 = 9 and an = 2a(n -1) - 3. Enter them in order (a1, a2, a3, a4, a5). This formula can be read as Next number = twice previous number subtract 3. Using this with a1 = 9, a2 = 15, a3 = 27, a4 = 51, and a5 = 99. 4). To find the nth term of a geometric sequence we use the formula: an = a1r^(n - 1) where r common ratio, a1 first term, and an - 1 the term before the n th term n = number of terms The given geometric series: -7 + 14 - 28 + 56 + ... an = a1r^(n - 1) = -7*(-2)^26 = -469762048 Sum of Terms in a Geometric Progression Finding the sum of terms in a geometric progression is easily obtained by applying the formula: nth partial sum of a geometric sequence Sn = a1(1 - r^n)/(1 - r), r not equaling 1 Find the sum S27 for the geometric series: -7 + 14 - 28 + 56 + ... a27 = -469762048 Sn = a1(1 - r^n)/(1 - r), S27 = -7(1 - (-2))^27/(1 + 2) = -7/3(1 + 134217728) = -313 174 701 5). Find the first three terms of the geometric sequence with a6 = 128 and a11 = -4096 128*r^5 = -4096 r^5 = -4096/128 r = (-32)^0.2 = -2 a6 = a1r^5 = 128 a11 = a1r^10 = -4096 a1(r^10 - r^5) = -4224 a1 = -4224/(1024 - (-32)) = -4224/1056 = -4 a2 = a1*2 = -4*-2 = 8 a3 = a2*r = 8*-2 = -16 http://answers.yahoo.com/question/index?qid=20120413065510AAKxm5V