Review of Sequences - Homework
an  a1  (n  1)d
Sn 
n
(a1  an )
2
an  a1r n 1
Sn 
a1 (1  r n )
1 r
 r
A  P 1  
 n
nt
1) What is the eighth term of the
Fibonacci sequence?
2) What is the 7th term of the sequence
defined as follows:
The first term is 9 and an  5an1  3
n2?
3) What is the 18th term of an arithmetic
sequence when the first term is 4 and
the common difference is 7? You must
use a formula.
for
4) For the sequence 2, 7, 12, 17,…
a) Write a formula for the nth term.
b) Find the 18th term of this sequence:
You must use a formula.
5) What is the sum of the first 70 terms of
an arithmetic sequence when the first
term is 15 and the common difference
is 3? You must use a formula.
6) Find the sum of the first 60 terms of
this sequence: You must use a formula.
12, 19, 26, 33…
7) Find this sum. You must use a formula. 8) What is the 12th term of a geometric
sequence when the first term is 4 and
60
the common ratio is 3? You must use a
6i

formula.
i 1
9) For the sequence 3, 12, 48, 192,…
a) Write a formula for the nth term.
10) Find the sum of the first 12 terms of
this sequence: You must use a formula.
5, 10, 20, 40,…
b) Find the 8th term of this sequence:
You must use a formula.
11) Find this sum. You must use a formula. 12) A job pays a salary of $36,000 the first
8
year. During the next 5 years, the
3( 4)i

salary increases by 2% each year. What
i1
is the total salary paid over the 5 year
period? Round your answer to the
nearest dollar. You must use a formula.
13) Use the graphs of the arithmetic sequences {an } and {bn } to find a15  b14
14) Projections for the U.S. population, ages 85 and older, are shown in the following
table.
a) Divide the population for each decade by the population in the preceding decade.
Show that the projected population is approximately a geometric sequence.
b) Write the general term of the geometric sequence describing the U.S. population
ages 85 and older, in millions, n decades after 2000.
c) Use the model in part b) above to project the U.S. population, ages 85 and older,
in 2090.