Answer to Question #161960 in Discrete Mathematics for gr

Question #161960

Write the first 4 terms of the following formula, start with n = 1.

  1. an = 5n
  2. nbn = 3!bn = 3n bn = 3n^2 +2n - 6
  3. gn = 1 × 2 × ... n
  4. c1 = 2.5, cn = cn-1 + 1.5
  5. d1 = -3, dn = -2dn-1 + 1
1
Expert's answer
2021-02-11T12:44:50-0500

Given sequences are:-

"1. a_n=5n\\\\"

at n=1, "a_1=5"

Similarly "a_2=10, a_3=15, a_4=20"

First four terms are "5,10, 15, 20."


2."nbn = 3!bn = 3n bn = 3n^2 +2n - 6"

at n=1

First term is "3(1)^2+2(1)-6=-1"

Similarly other terms at "n=2,3,4" are "10,27,50"

First four terms are "-1,10,27,50"


3."g_n=1\\times2..\\times n"

at n=1, "g_1=1"

Similarly at n=2,3,4

"g_2=2,g_3=6,g_4=24"


First four terms are "1,2,6,24"


4."c_1=2.5, c_n=c_{n-1}+1.5"

at n=2, "c_2=c_1+1.5=2.5+1.5=4"

at n=3, "c_3=c_2+1.5=4+1.5=5.5"

at n=4, "c_4=c_3+1.5=5.5+1.5=7"

First four terms are "2.5,4,5.5,7"


5."d_1=-3,d_n=-2d_{n-1}+1"

at n=2, "d_2=-2d_1+1=-2(-3)+1=7"

at n=3, "d_3=-2d_2+1=-2(7)+1=-13"

at n=4, "d_4=-2d_3+1=-2(-13)+1=27"

First Four terms are "-3, 7, -13,27"


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