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):
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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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