Question

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.

Answer #1

For an arithmetic sequence, a34=20. If the common difference is
-5, find:
First term:
Sum of first 66 terms:

1. Write the explicit rules for the following sequences:
A) 1/2, 2/5, 3/10, 4/17, 5/26, 6/37,.....
B) 3, -5/1, 7/6, 9/24, 11/120,...
2. Given two terms of the arithmetic sequence find the common
difference, the first term, and the explicit formula ( a subscript
n)
a) a subscript 17= 105
a subscript 40 = -30
b) a subscript 10
a subscript 40= 100
b)

The sum of the first 14 terms of an arithmetic sequence of real
numbers is 20 and the sum of the next 20 terms is 14. Find the
largest positive integer K for which the sum of the first K terms
of this sequence is positive.

1 .Answer the following questions about the arithmetic sequence
2, 5, 8, 11, .... . Find n if the series 2 + 5 + 8 + 11 + ⋯ + 119 =
2420.
2. Answer the following questions about the geometric sequence
3, 12, 48, 192. Which term in the sequence is 12288?
3. Find the sum of the series 106 + 103 + 100 + 97 + ⋯ − 41.
4.Find S7 and S∞ for the series 6 +...

1) The twelfth term of an arithmetic sequence is 118, and the
eighth term is 146. Find the nth term. (3 points)
2) A partial sum of a geometric sequence is given. Find the sum.
(3 points)
3) Determine wether the given infinite geometric series is
convergent or divergent. If the series is convergent, then find its
sum. (4 points)
a) b)

Given two terms in an arithmetic sequence find the
common difference, the 52nd term, and the explicit
formula.
a11 = -
325 and a39 = - 1165

Write a recursive formula for an arithmetic sequence whose 4th
term is 5 and whose 7th term is -22. a)a↓1=32, a↓n=a↓n-1-9
b)a↓1=32, a↓n=a↓n-1-27 c)a↓1=56, a↓n=a↓n-1-17 d)a↓1=5,
a↓n=a↓n-1-22

We are given a sequence of numbers: 1, 3, 5, 7, 9, . . . and
want to prove that the closed formula for
the sequence is an = 2n – 1.
What would the next number in the sequence be?
What is the recursive formula for the
sequence?
Is the closed formula true for
a1?
What about a2?
What about a3?
Critical Thinking
How many values would we have to check before we could be sure
that the...

For the sequence 8x + 4, 7x + 3, 6x + 2, 5x +1, ... ,
a. Identify the next 3 terms.
b. Is the sequence arithmetic or geometric? How do you know?
c. Find the explicit and recursive formulae for this
sequence.
d. Write out the sum formula for the first 20 terms and
evaluate.
e. Write your process to part (d) in Sigma Notation.

Translate the following phrases into algebraic expressions:
a. The 9th term of an arithmetic sequence whose
first term is 10 and whose difference is d
b. 9 less than twice a number
c. 9 times the square of a number
d. The difference between the cube of a number
and twice the number

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