Posted by lee on Tuesday, February 12, 2013 at 11:29am.
I have 3 questions I need help with.
1) what is the 15th term of the sequence 81,27,9,...
2) what is a possible value for the missing term of the geometric sequence 39,_,975,_
3) what is the sum of the finite arithmetic series (5)+0+5+10+..+65

algebra  Reiny, Tuesday, February 12, 2013 at 12:29pm
your first sequence looks geometric with
a = 81, r = 1/3
term(15) = ar^14
= 81(1/4782969)
= 1/59049
2. let the missing term be x
then x/39 = 975/x
x^2 = 38025
x = ± √38025 = ± 195
could be 195 or 195
3. looks arithmetic with a = 5 , d = 5
term(n) = 65
5 + (n1)(5) = 65
5n  5 = 70
5n = 75
so we have 15 terms
sum(15) = (15/2)(first + last)
= 15/2(5+65) = 450

algebra  lee, Tuesday, February 12, 2013 at 1:22pm
the first and second is not a possible answer.
1) 1/729
1/243
1/81
1/810

algebra  Reiny, Tuesday, February 12, 2013 at 5:26pm
1. proof that my answer is correct
81 27 9 3 1 1/3 1/9 1/27 1/81 1/243 1/729 1/2187 1/6561 1/19683 1/59049
count the terms
2. proof my answer is correct:
195/39 = 5
975/195 = 5
195/39  5
975/195 = 5
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