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 + (n-1)(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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