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? Answer: Show work in this space. You can

Question 59091: Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer:
Show work in this space.
You can this r easily by taking the ratios

b) Using the formula for the nth term of a geometric sequence, what is the 10th term?
Answer:
Show work in this space.

c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?
Answer:
Show work in this space.

Found 2 solutions by funmath, jayanthi:
Answer by funmath(2873) (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?
Answer: r=3
Show work in this space.
r=a2/a1=a3/a2=a4/a3 they all have the same ratio.
r=3/1=9/3=27/3=3
:

b) Using the formula for the nth term of a geometric sequence, what is the 10th term?
Answer: a10=19683
Show work in this space.
an=a1*r^(n-1)
a10=1(3)^(10-1)
a10=3^9
a10=19683
:
c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?
Answer: S10=29524
Show work in this space.
Sn=a1(1-r^n)/(1-r)
S10=1(1-3^10)/(1-3)
S10=(1-59049)/-2
S10=-59048/-2
S10=29524
:
Happy Calculating!!!

Answer by jayanthi(5) (Show Source):
You can put this solution on YOUR website!
a.
3/1 = 9/3 = 27/9 R = 3
b.
Tn (Nth Term) = ar^n-1
a=3 n=10
T10= 1 * 3^10-1 = 3^9
C.
Sn = ar^n-1/r - 1
= 1*3^9/3-1 = 3^9/2