Create an explicit equation for the recursively-defined sequence below. **Optional table** to help convert the recursive equation to explicit: a1=4; an+1=D-3 a(n) 1. a(n) = Submit 3.

Q: Find the sixth term of a geometric sequence whose second term is 3 and whose fourth term is 1/3.…

A: Now dividing equation (2) by equation (1), we get Therefore sixth term is,

Q: Write the first five terms of the sequence whose general term is an=2/n factorial

A: From provided information, term is given as:

Q: Find the nth term an of a sequence whose first four terms are given. 2, 4, 8, 16,....

A:

Q: Create an explicit equation for the recursively-defined sequence below. **Optional table** to help…

A: t1=15,tn+1=3·tn So, n=0 gives t1=3·t0                   ⇒15=3·t0                   ⇒t0=153=5

Q: Find the infinite sum of the geometric sequence with a1 = 3, r = if it exists. 8

A:

Q: Write a rule for the n th term of the geometric sequence for which a, = 64 and a,=1.

A: Solving by geometric sequence we have

Q: Determine the sum of the first four terms of the geometric sequence where a = 3 and r = 2.

A:

Q: Find the sum of the first 14 terms of the geometric sequence: - 3/2, 3, -6, 12, . . . .

A: The given geometric sequence is -32,3,-6,12,.. here the first term of the sequence is -32. find…

Q: Find two different explicit formulas for the sequence{ -1, 1, -1, 1, -1, 1, ⋅ ⋅ ⋅}.

A: Given: Sequence: {-1, 1, -1, 1, -1……. } 1) It is an infinite geometric progression in which:…

Q: Determine if the sequence converges or diverges. -30,-14,-6,-2,0,…

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Q: Determine the sum of the geometric sequence if it exist. If the sum does not exist, write DNE. 8,…

A: Given,            A sequence is 8,-12,18,27,.....We know that,           A sequence is in Geometric…

Q: What are the next three terms of the geometric sequence 3, 12, 48, . . . ?

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Q: Find the 12th term of the geometric sequence 5, 20, 80, ...

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Q: Find the sum of the first 8 terms of the sequence defined by a, = 4- 3"-1

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Q: 2. The missing term of the geometric sequence 45, [ ],1620, . is ...

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Q: Find the specified term of the geometric sequence. 6th term: 5, 15, 45, . . .

A: sequence is 5,15,45,......... first term, a1 = 5 r = a2/a1    = 15/5     = 3

Q: Find the infinite sum of the geometric sequence with 2 if it exists. 7 a = 4, r = -

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Q: Find the sixth term of the geometric sequence whose first two terms are 4 and 6.

A: There are many names if the set of numbers follows a specific pattern to write the terms. They are…

Q: Calculate the 10th term for this arithmetic sequence: 4, 1, -2, -5, ..

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Q: Identify the 7th term of the sequence: 4, 20, 100, .... * O 65,200 315,200 O 62,500 O 312,500

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Q: Find the sum of the first 4 terms of a geometric sequence with a = 270 and r= The sum is 2/3

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Q: Here are the first two terms of a geometric sequence: 2, 4. What are the next three terms?

A: First-term, a=2 Common ratio, r = 4/2 = 2

Q: Find the 10th term of the geometric sequence. aj1 = -5, r = - %3D %3D 10th term:

A: →nth term any geometric sequence is given by,                            an = a1 rn-1 , Where a1  is…

Q: Write the first five terms of the geometric sequence whose first term is 8, and whose common ratio…

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Q: write the first five terms of the sequence defined recursively. a, = 15, akti =(-3)aK %3D KtI

A: Given a1=15 and ak+1=-3(ak)So the first 5 terms of the sequence will be a1,a2,a3,a4,a5

Q: Find the infinite sum of the geometric sequence with 2 if it exists. 8 6, г a = -

A: The geometric sequence with a=6, r=28

Q: Write the first four terms of the sequence whose general term is given. an = 4n + 4

A: Here, for given sequence we have to find first four terms.

Q: Find the first four terms of the sequence defined by а, — 3 %3D а, 3 За, —1 + 2, for all n > 1

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Q: Find the infinite sum of the geometric sequence with a = = 6, r = if it exists. %3D 2 00

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Q: Which arithmetic sequence has a first term equal to 47 and a common difference of -18?

A: To find the arithmetic sequence

Q: Create the first terms of a sequence using the following recursive definition (see image attached).…

A: We use the given general term of the sequence to find first few terms of the sequence.

Q: Find the infinite sum of the geometric sequence with a =2 r=2/6 if it exist

A: The geometric sequence with a =2, common ratio r=2/6

Q: Find the 10th term of the geometric sequence. If your answer is a fraction, enter it like: 1/2, etc.…

A: I have given an answer in step 2.

Q: Find the nth term of a sequence whose first several terms are given. 4, -16, 64, -256, ... an II

A: nth term of sequence.

Q: 4, _, 100, ..

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Q: List the first five terms of the sequence defined by An = (-1)".10"-1 %3D

A: SOLUTION-

Q: Find the 13th term of the geometric sequence 7, 21,63, ...

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Q: Find the number of terms in the geometric sequence 16, 8, 4, 2, ... , 16

A: The nth term of the GP with a as the first term, r as the common ratio is given by, an=arn-1

Q: Find the 9th term of the geometric sequence 8, 32, 128, ...

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Q: Find a closed formula for the sequence with recursive definition An = 2an-1 – an-2 with a1 = 1 and…

A: The closed formula for a sequence is used to define the general term of a sequence. The recursive…

Q: Write the first four terms of sequence whose general term is given an = 3n + 2.

A: Given: an=3n+2 To Find: First four term of the sequence whose general term is given.

Q: Find the nth term of a sequence whose first several terms are given. 7, 2, –3, –8, ... an

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Q: Find the 6th term of a geometric sequence with a 1 = −3 and r= 2.

A: Find the 6th term of a geometric sequence with:

Q: Find the infinite sum of the geometric sequence with a = 6, r = if it exists. %3D %3D

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Q: Write the first 5 terms of the sequence that follows this recursive rule. a1 = 4 an = an-1 -3

A: Given that  As per our policy we can answer only 1 question.

Q: What are the first five terms of a geometric sequence with a = 3 and r = 2?

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Q: Determine the sum of the first five terms of the geometric sequence where a = 3 and r=2. ... The sum…

A: The formula to evaluate the sum of n terms of a geometric sequence is Sn=arn-1r-1, if r≠1, where a…

Q: Determine the sum of the first four terms of the geometric sequence where a = 3 and r= -1. The sum…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.