Question

1. Find the limit of the sequence whose terms are given by an=
(n^2)(1-cos(5.6/n))

2. for the sequence an= 2(an-1 - 2) and a1=3

the first term is?

the second term is?

the third term is?

the forth term is?

the fifth term is?

Answer #1

1. For the sequence an=9+(−1)^n
its first term is
its second term is
its third term is
its fourth term is
its 100th term is
2. Find a formula for the general term an of the sequence
assuming the pattern of the first few terms continues.
{4/3, 4/9, 4/27, 4/81, 4/243, ⋯}
Assume the first term is a1
an =

Find the first, second, third, fourth, and fifth term for
each...
a)For the sequence an=an−1+an−2an=an−1+an−2 and
a1=1,a2=2a1=1,a2=2,
b) a1=−1; an+1=−2an−1
c) an=2(an−1−2)an=2(an−1−2) and a1=5a1=5,
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write the first 4 terms of the sequence whose nth term is given
by the formula:
an= n− 2/n

Write out the first five terms of the sequence with
{[(n+8)/n+1)]^n}^inf n=1 and find its limit as well as mention if
it converges?

Determine the Convergence or Divergence of the sequence with the
given n- th term. If the converges find the limit.
a.) an= (-3/7)n+4
b.) an= nsin(1/n)
c.) an= cos n?

A sequence has a recursive formula of an = (-2)n (an-1) for n≥2.
The fourth term a4 is 1,536.
a. Find the first term a1. (5 points)
b. Find the sixth term a6. (5 points)

1. Find the first six terms of the recursively defined
sequence
Sn=3S(n−1)+2 for n>1, and S1=1
first six terms =

The first difference of a sequence is the arithmetic sequence 1,
3, 5, 7, 9, .... Find the first six terms of the original sequence
in each of the following cases.
a. The first term of the original sequence is 2.
b. The sum of the first two terms in the original sequence is
9.
c. The fifth term in the original sequence is 32.

Let a1= - 1 , an+1= (6+an) /
(2+an).
a) Assume that the given recursive sequence is convergent. Find
the limit.
b) Is the given sequence bounded? Why?

1)
Write nth term suggested by pattern.
1, 1/4, 1/16, 1/64, ...
2) Find first term (a1), the common difference (d), and give a
recursive formula (an) for sequence.
8th term is 55; 15th term is 118
3) Find the nth term and the indicated term of arithmetic
sequence whose initial term and common difference are given.
first term=6
common diff= -10
nth term?
13th term?

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