Here is a pattern where the number of small squares increases with each new step. Step 1 Step 2 Step 3 1. Write a recursive definition for the total number of small squares S(n) in Step n. 2. Sketch a graph of S that shows Steps 1 to 7. 3. Is this sequence geometric, arithmetic, or neither? Be prepared to explain how you know.

Q: Find the 12th term of the geometric sequence 1, –4, 16, ...

A: Given  Geometric sequence   1,-4,16..... To do find the 12th term of the given sequence.

Q: Write an explicit rule for each geometric sequence using subscript notation. Use a calculator and…

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Q: Part A: Mrs. Bitter writes the two following sequences on the board, then asks you to explain to…

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Q: The first term of an arithmetic sequence is 5. The third term of the sequence is 13. Which of the…

A: Given,First term of AP = a = 5Third term of AP= 13Let, Second term of AP = xWe can write AP as - 5,…

Q: Use the nth term of an arithmetic sequence an = a1 + (n-1)d to answer this question. Thank you and…

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Q: Create a rule for a geometric sequence given the following information: a3 = 6, r = value of a1 : a1…

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Q: Find the 20"" term of the arithmetic sequence whose common difference is d= 5 and whose first term…

A: The formula to find the nth term in arithmetic sequence is given below: an=a1+n-1d where, a1 is the…

Q: The sequence is defined recursively. Write the first four terms. 1) a1 = 5; an = an-1- 4

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Q: Given the recursive rule for an arithmetic sequence, write the explicit rule. 5. f(1) = 19 and f(n)…

A: Question number 5,Given,          f1=19 and fn=fn-1-10 for n≥2

Q: Find the first four terms of the arithmetic sequence. a1 = -9, d= 8 What is the first term? a1 -

A: Consider the provided information, a1=-9  and d=8 Find the first four terms of the sequence. Using…

Q: Find thr next three term in the sequence. You must show your work 2, 6, 11, 17, _, _, _

A: To find the next terms of the sequence, first check the pattern of getting successive term from the…

Q: Find the 16"" term of the arithmetic sequence whose common difference is d= 8 and whose first term…

A: The first term of the arithmetic sequence is 2 and common difference is 8. To find the 16th term of…

Q: Find ag and a, for the arithmetic sequence. a,=x, a, = x+3

A: a1=x , a2=x+3 Formula an=a1+(n-1)dd is the common difference

Q: The sequence shown below is defined using a recursion formula. Write the first four terms of the…

A: Given sequence shown above is defined using a regression formula.We find first 4 terms of the…

Q: The general term of a sequence is given and involves a factorial. Write the first four terms of the…

A: Given:            an=n+1!n2 We calculate first four terms of the sequence, n=1, 2, 3 and 4…

Q: Given the explicit rule for an arithmetic sequence, write the recursive rule.

A: We have given the explicit form of the arithmetic sequence , we need to write their recursive rule…

Q: Consider the sequence whose nth term is an = 4n - 3. Find a2 - a1, a3 - a2, a4 - a3, and a5 - a4.…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Suppose that tn is an arithmetic sequence. Find the values of a and d if we know that t10 38 and t15…

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Q: If the general term of an arithmetic sequence is :- 1 2n. T(n) = %3D then the

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Q: Write a recursive sequence that represents the sequence defined by the following explicit formula:…

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Q: The first term of an arithmetic sequence is a = 7, and the common difference is d = 3. How many…

A: Given: for given arithmetic sequence, first term a=7, common differenced=3 let's sum of n terms of…

Q: The first three terms of a geometric sequence are as follows. 81. 27,9 Find the next two terms of…

A: Our objective is to find the next to turn of the geometric sequence.

Q: Consider the sequence whose nth term is an = 3 . 5n.Find a2/a1, a3/a2, a4/a3, and a5/a4. What do you…

A: Given: The sequence whose nth term is an=3×5n. To find: a2a1, a3a2,a4a3,a5a4.

Q: Answer the following questions about the sequence an = -2n + n 1. Is the sequence increasing or…

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Q: The sequence is defined recursively. Write the first four terms. a1 = 1 and an = an-1 - 3 for n ≥ 2

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Q: Write the recursive formula for the geometric sequence below 7 49 3 3 1 1 21' 3' A(1) = A(n) = A(n-…

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Q: rd Find the 23' term of the arithmetic sequence whose common difference is d=3 and whose first term…

A: We know that nth term of an arthmetic series is given by - an = a1 + (n-1)d. Here a1 = first term ;…

Q: The sequence shown below is defined using a recursion formula. Write the first four terms of the…

A: Solve

Q: Jse a graphing calculator to construct a table of values and a graph for the first 10 terms of the…

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Q: 1. Write a recursive definition for the total number of small squares S(n) in Step n. 2. Sketch a…

A: 1. In the first step, there is only one small square. In the second step, a large square which has…

Q: 1. Write out the next 4 terms of the sequence a = a,' +n-1; a, =1 (this means %3D а, а,, а,, а,).

A: Given a0=1 and an+1=an3+n-1a1 means n=0So, a1=a0+1=13+0-1          =0a2=a1+1=03+1+-1              =0

Q: Find the 15"" term of the arithmetic sequence whose common difference is d =6 and whose first term…

A: an = a  + (n-1)d

Q: Find a, and a3 for the following geometric sequence. a, =3, r= -2 an %3D

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Q: Write out the first four terms of the sequence given the following recursive definition: tne1 =…

A: # the given initial value is a1=8 . considering it as t1=8 given the relation tn+1=-2tn+6 substitute…

Q: A sequence is shown in picture form. Assume that the sequence continues to grow in the same way.…

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Q: Write the first four terms of a sequence given the following information: a: = -2 and the recursive…

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Q: Find a n for the geometric sequence a 1 =-4; r = - 2, n = 10

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Q: Write the first five terms of the sequence defined recursively. a₁ = 5, ak+1 = 4(a-3) ak+1 a₁ az 33…

A: We will find the required.

Q: If you were to shade in a n × n square on graph paper, you could do it the boring way with sides…

A: Given, if you were to shade in a n × n square on graph paper, you could do it the boring way with…

Q: After Roger's surgery, his doctor administered pain medication in the following amounts in…

A: A recursive formula is a formula that defines each term of a sequence using preceding term…

Q: The sequence shown below is defined using a recursion formula. Write the first four terms of the…

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Q: Write a recursive sequence that represents the sequence defined by the following explicit formula:…

A: topic- sequence and series

Q: The general term of a sequence is given an = -2(n - 1)! and involves a factorial. Write the first…

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Q: Find the nth term of a sequence whose first several terms are given. 10 11 9' 10' 11' 12' an = Need…

A: The given sequence is 89,910,1011,1112,....

Q: Given the first term and the common difference of an arithmetic sequence find explicit rule and the…

A: The given data are first term of AP and the common difference a1=12 d= 10 We know the formula of AP…

Q: Find the explicit formula for the arithmetic sequence Bn given the information below. b1=2 b4=-13

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Q: Find the 19" term of the arithmetic sequence whose common difference is d=3 and whose first term is…

A: the nth term of the arithmetic sequence is given by an=a1+n-1d here we have a1=4,   d=3 an=4+n-13…

Q: Consider the sequence whose nth term is an = 4n - 3.Find a2 - a1, a3 - a2, a4 - a3, and a5 - a4.…

A: an=4n-3. Put n=1, 2, 3, 4, 5 in an=4n-3, we get a1=41-3=1a2=42-3=5a3=43-3=9a4=44-3=13a5=45-3=17

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: Jordi is trying to decide if the following table and corresponding graph represent a geometric or…

A: Sequence

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.