A sequence a1, a2, a3,….. is defined by An+1 4аn — 3, п > 1 -- = k, where k is a positive integer. Given that E3_ a, = 66, find the value of k.

Q: The 2 – tail of the sequence Y = (1, 3, 5, 7, 9,... , 2n – 1, . ..) is: O Y = (7,9,..., 2n + 5, ...)…

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Q: Suppose that n > 5 and that the numbers t1, t2, t3, . . . , tn−2, tn−1, tn form an arithmetic…

A: We need to determine the value of n in the given arithmetic sequence.

Q: Find the sum of the first EIGHTEEN terms of the given sequence where - is the eighteenth term. *If…

A: Topic:- sequence and series

Q: The eight term in a geometric sequence with a second term 3 and fifth term 81/8, multiply with the…

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Q: Find the sum of the first 130 terms of the arithmetic sequence 8, , 7, ....

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Q: Give the first three terms of each sequence based on the given a1=4,         r=-2         _____,…

A: To find the first three terms of each sequence

Q: An IT company labels its products by sequences of 4 symbols which are either capital letters or…

A: The number of ways of selecting r things from a total number of n things is given by the expression…

Q: Show that the sequence 9,12,15,18, ... is an AP. Find its 16th term and the general term.

A: We need to show that the sequence 9, 12, 15, 18, ... is an AP. Here, 12 - 9 = 15 - 12 = 3. And the…

Q: Find the Sum to infinity of the sea tès - Ce30 t ces 20 - 1-3 1-3.5 ces 30 + - (-nCBCIT). 2.4 2.4-6

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Q: Find at least three different sequences beginning with the terms 1, 3, 9 whose terms are generated…

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Q: Suppose that the sequence {ak}1 is 2, 4, 6, 8, 10, 12, 14, 16, . What is a,?

A: we have the given sequence 2,4,6,8,10,12,14,16,...

Q: 6. Determine if the sequence is geometnc. DRHIS,find the comman fatio. an-1,3,-1.. ماتوقو

A: Given: 27,-9,3,-1,..............

Q: Find the sum of the first eight terms of the sequence 1/8,−1/4 ,1/2 ,.... please show working

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Q: What are the first 5 terms in the sequence aj = 5 An = an-1 +4

A: Given sequence is  a1=5an=an-1+4

Q: What is the sum of the first 10 terms of the sequence {300, 150, 75, ...}?

A: Given: 300,150,75,...... Formula Used: Sn=a1-rn1-r

Q: Here is a rule to make a list of numbers: Each number is 4 less than 3 times the previous number. 1.…

A: Here is a rule to a  list  of numbers  Each  number  is  4 less than  3 timesthe    previous number.…

Q: 1 1 az = 125 sin 25 1 1 az = 3125 sin 1 a1 = 5 sin az = 25 sin 53 a4 125 625 sin 625 3125 a) Find an…

A: Given:

Q: Construct a difference table to predict the next term of the sequence.   10, 10, 12, 16, 22, 30,…

A: 10, 10, 12, 16, 22, 30;

Q: If 77, 49 , 36 are my first three terms of the sequence what are my next two and what is the rule

A: The first three terms of the sequence are 77, 49, 36. Find the next two terms as follows.

Q: The first five terms of the sequence tn = 1(1/3)n-1 are: If necessary, express terms as improper…

A: We can find the required terms as below.

Q: Find the next two terms in th. sequence. 8, 5, 2, -1, -4, [ ? ].[ ]

A: Given sequence is : 8, 5, 2, -1, -4 To find the next two terms in this sequence.

Q: Find the 9th term for the sequence of positive 3 digit numbers that are multiples of 5.

A: We have to find the 9th term for the sequence of positive 3 digit numbers that are multiples of 5…

Q: Which sequence could be described by the first term: Aj = 1 and the recursive (an)² + 1 definition:…

A: Given, an+1=an2+1 a1=1

Q: Terms of the sequence a1, a2, a3, . .. , a2020 are obtained by the rule: 1+a1 1+ a2 1+ a2019 az = 1-…

A: Reciprocal of a number n is 1n.

Q: Find the number of strings of length 8 of lower case letters of the alphabet, with repeated letters…

A: The length of the string is 8 and one letter are given , begin with v or end with f. We have to…

Q: Determine the first five terms of the sequence whose nth term is defined as follow.  ann=(1/2)n-1-8

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Q: 10. a, = 6, ant1 an

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Q: Suppose that the sequence {ax} is =0 2, 4, 6, 8, 10, 12, 14, 16, .. What is a1?

A: The given sequence {ak}k=0∞ is -  {ak}k=0∞ = 2,4,6,8,10,12,14,16,18,......... The first tern of the…

Q: ,(n+), Does the sequences eventually increasing or decreasing ? (2n² – 7n) , (n³ – 4n²), (- , (n +…

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Q: Suppose that the sequence {ax}ı is k= 1,3, 5, 7, 9, 11, 13,.. What is a;?

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Q: What is the 100th term of a sequence of number in which, for every positive integer x, the sum of…

A: In the given question, concept of summation series is used. Summation Series The total of the series…

Q: , n=1,2,3. is a sequence of real numbers defined by a, = /2 %3D %3D and for n21, a = 2,/2+a, .

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Q: Supposed vn =17-n2  is the explicit specification for a sequence. How many values of n (positive)…

A: Given: Vn=17-n2

Q: Arrange the integers 1,2,3, . . . ,23 so that the sum of consecutive numbers is equal to a perfect…

A: Given,  We have to   Arrange the integers 1,2,3, . . . ,23 so that the sum of consecutive numbers is…

Q: A MAT212 student used pen, paper and a handheld scientific calculator to apply an entrapment…

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Q: The first four terms of the sequence defined by an пап 1+ п'а, 2, @о — 3, а, — 4 are %3D aо — 3, ај…

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Q: If the sequence if geometric, match it to its correct explicit formula, a, If it not geometric,…

A: If the sequence is geometric, we will match it to its correct explicit formula, an. (i) 4, 6, 8, ...…

Q: Write the first 7 terms of the Fibonacci type sequence begging with 5,3. State as an exact radical…

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Q: Show that the sequence too n! 217 is eventually strictly increasing or eventually strictly…

A: The given sequence is n!21nn=1∞ Eventually strictly increasing sequence : A sequence is said to be…

Q: Find the sum of the infinite geometric series if it exists.

A: To find: The sum of given infinite geometric series. Given information: The series is 1-12+14-18+⋯…

Q: Suppose that the sequence {az}ı is k=1 1,3, 5, 7,9, 11, 13,.. What is a1?

A: First we find the general of the given sequence {ak}∞k=1=1,3,5,7,9,11,13,..., with the help of…

Q: A sequence a1, a2, a3,.... satisfies the property that an+1 is the average of the first n terms if…

A: We have to find a2 .

Q: Find x and y such that 5, x, y,32 is part of an arithmetic sequence. Then find x and y so that the…

A: Given sequence is 5,x,y,32. First find the value of x and y such that sequence 5,x,y,32 is a part of…

Q: the sum of the first 40 terms of the arithmetic sequence.   −16​,−25​,−34​,−43​,...

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Q: A Diginacci sequence is created as follows: The first two terms are any positive whole numbers Each…

A: Given are the instructions to form a Diginacci sequence: The first two terms are any positive whole…

Q: Consider the sequence 81, 27, 9, 3, 1,... and find the sum of the first five terms. Please provide…

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Q: Decide whether the sequence 1, 2, 3, 4, 5, 6, 7,. is finite or infinite. ..... Choose the correct…

A: Given:      1 , 2 , 3 , 4 , 5 , 6 , 7 ........

Q: )In the sequence 2, 5 , 8, 11, 14, .. , the common, =) In the sequence 2, 5, 8, 11, 14, .. , the…

A: Given query is to find the value of indicated terms.

Q: If 40 participants are randomly selected to 4 groups of 10, does the 40 comes first in the sequence:…

A: Given: If 40 participants are randomly selected to 4 groups of 10, does the 40 comes first in the…

Q: Find the indicated term of following sequence  1,1,-3,5,-7,9 ,---------a10 1,3,12,60---------a6

A: In this problem, we have to identify the relationship between the successive terms of the series to…