MATH 1151 – Chapter 12 Problems
1.) Write down the first 5 terms of the sequence{ }
{
2.) Write down the first 5 terms of the sequence { }
{
3.) Write down the nth term of a sequence {
}.
}.
} suggested by the pattern
4.) Write down the first five terms of a recursively defined sequence with a1 = 3 and an = 4 – an-1.
5.) Write down the first five terms of a recursively defined sequence with a1=-1, a2=1, and an=an-2+nan-1.
6.) Write out the sum ∑
7.) Write out the sum ∑
.
.
8.) Express each sum using summation notation.
a.) 1 + 2 + 3 + . . . + 20
9.) Find the sum of each sequence.
a.) ∑
b.)
b.) ∑
10.) Find the nth term of the arithmetic sequence {
What is the 51st term?
a.) a1 = -2; d = 4
} whose initial term a and common difference d are given.
b.) a1=1; d =
11.) Find the 80th term of -1, 1, 3, . . .
12.) Find the first term and the common difference of the arithmetic sequence described. Give a recursive formula for
the sequence. Find a formula for the nth term.
a.) 8th term is 4; 18th term is -96
b.) 5th term is -2; 13th term is 30
13.) Find each sum.
a.) 7 + 1 – 5 -11 - … - 299
b.) 2 + 5 + 8 + … + 41
c.) ∑
14.) Find x so that 2x, 3x + 2, and 5x + 3 are consecutive terms of an arithmetic sequence.
15.) Find the fifth term of the geometric sequence whose initial term a1 and common ratio r are given.
a.) a1 = -2; r = 4
b.) a1 = 1; r =
16.) Find the 10th term of -1, 2, -4, …
17.) Find the nth term, an of each geometric sequence.
a.) 4, 1,
,…
18.) Find the sum of
19.) Does the infinite sequence of ∑
b.) a6 = 243; r = -3
c.) a3 = ; a6 =
.
converge or diverge? If it converges, find its sum.