Pre-Calculus 11
Unit 1 Sequence and Series Review.
1. Are the following sequences arithmetic, geometric, or neither? If they are
arithmetic, state the value of d. If they are geometric, state r.
2. Write the general term of tn and Sn below in their simplest forms
2. Find the sum of each of the Arithmetic Series below
3. An arithmetic sequence has 5 and 13 as its first two terms respectively.
a. Write down, in terms of n, an expression for the nth term, tn .
b. Find the number of terms of the sequence which are less than 400.
4. In an arithmetic sequence, the first term is 5 and the fourth term is 40. Find the
second term.
5. In an arithmetic sequence, the first term is –2, the fourth term is 16, and the nth
term is 11 998.
a. Find the common difference d.
b. Find the value of n.
6. Consider the arithmetic series 2 + 5 + 8 +....
a. Find an expression for Sn, the sum of the first n terms.
b. Find the value of n for which Sn = 1365.
7. The first three terms of an arithmetic sequence are 7, 9.5, 12.
a. What is the 41st term of the sequence?
b. What is the sum of the first 101 terms of the sequence?
8. Let Sn be the sum of the first n terms of an arithmetic sequence, whose first three
terms are t1, t2 and t3. It is known that S1 = 7, and S2 = 18.
a. Determine
t1.
b. Calculate the common difference of the sequence.
c. Calculate t4.
9. The second term of an arithmetic sequence is – 12 and the sum of the first twelve
terms is 18. Find the 6th term.
t2 = –12 = t1 + d
S12 =
-------> t1 = –12 – d,
Since t1 is not given, so we need to
find t1 in relation to d.
12
2 t 1(12  1)d   62  (12  d )  11d 
2
S12 = 18 = 62  (12  d )  11d 
÷6
÷6
t1 = –12 – d = –12 – 3 = –15
t6 = –15 + 5(3) = 0
--------->
substitute (–12 – d ) for t1
3 = –24 –2 d + 11 d
3 = –24 + 9 d solve for d.
27 = 9 d,
3 = d.
10. The first three terms of an arithmetic sequence are: p, 2p – 4, 2p + 3. Find
a. the common difference
b. the first term.
11. For the following geometric sequences, find t1 and r and state the formula for the
general term.
a) 1, 3, 9, 27, ...
b) 12, 6, 3, 1.5, ...
c) 9, –3, 1, ...
12. Use your formula from question 11c) to find the values of the t4 and t12
13. Find three integers that have a sum of 27, a product of 288, and form an
arithmetic sequence.
,d=7
Because
and
2 + 9 + 16 = 27
(2)(9)(16) = 288
14. Determine the value of the following infinite series.