SOLUTION: Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following: a) What is r, the ratio between 2 consecutive terms? b) Using the formula for the nth term of a g

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Question 78348: Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following:
a) What is r, the ratio between 2 consecutive terms?
b) Using the formula for the nth term of a geometric sequence, what is the 10th term?
c) Using the formula for the sum of a geometric sequence, what is the sum of the first 10 terms?

Answer by rmromero(383)   (Show Source): You can put this solution on YOUR website!

Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following:
a) What is r, the ratio between 2 consecutive terms?
a[k+1]
r = ________
a[k]
3 9
= _____ = 3, _____ = 3 , hence r = 3
1 3
b) Using the formula for the nth term of a geometric sequence, what is the 10th term?
=
n = 10, r = 3, = 1
=
= 1 (3^9)
= 19683
c) Using the formula for the sum of a geometric sequence, what is the sum of the first 10 terms?
()
= _____________
r - 1
Where r = 3, n = 10, = 1

1 ()
= _____________
3 - 1

1 (59049 - 1)
= ________________
2
59048
= _________
2
= 29524
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