The nth term of an arithmetic sequence is given. an =- (n - 1) (a) Find the first five terms of the sequence. a = a2 = az = a4 = a5 = (b) What is the common difference d? d =

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: 1. The first term of an arithmetic sequence is 5. The eleventh term is 125. What is the common…

A: GivenFirst term of arithmetic sequence 'a' = 5Eleventh term of arithemetic sequece 'T_11' = 125

Q: What is the explicit equation for the nth term of the arithmetic sequence 6, 3.5, 1,-1.5, 4,...?…

A: We have: a1=6 -- the first term   Next, we calculate the common difference d=a2-a1 So, we have:…

Q: Find the missing terms of the sequence and determine if the sequence is arithmetic,

A: Sequence is said to be geometric when it has common ratio and arithmetic when it has common…

Q: Write an expression that gives the requested term. The 12th term of the geometric sequence with…

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Q: For an arithmetic sequence, a25 32. If the common difference is 1, find: a1 = the sum of the first…

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Q: Write an expression for the geometric sequence with first term a = 3 and common ratio r =1/ 2 . Give…

A: An expression for the geometric sequence with first term a = 3 and common ratio r =1/ 2 will be =…

Q: Write the first five terms of the geometric sequence with the given first term, a,, and common…

A: Let's find.

Q: Show that the sequence is arithmetic. Find the common difference, and write out the first four…

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Q: What is a sequence? What notation do we use to denote the terms of a sequence?

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Q: Use the formula for the sum of the first n terms of a geometric sequence to solve:A pendulum swings…

A: As per the question,                    We are given the geometric sequence which the pendulum…

Q: ind the 85th term of the arithmetic sequence with first term 1 and common difference -1/2

A: As we know that the expression for the nth term of the arithmetic sequence is: Tn=a+n-1d Where 'a'…

Q: Which geometric sequence has a first term equal to 55 and a common ratio of -5?

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Q: QI. Write out the first four terms of the sequence and determine whether the sequence is converging.…

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Q: an arithmetic sequence is 75 and the second term is 11 Find the first term.

A: Here I am providing the handwritten solution

Q: Write an expression that gives the requested term. The 11th term of the geometric sequence with…

A: We have to write an expression that gives the requested term.

Q: Write an expression that gives the requested term. The 16th term of the geometric sequence with…

A: To determine the 16th term of the series.

Q: What is the 12th term in the geometric sequence -9,27,-81...? A) -531441 B) 1594323 C) -4782969 D)…

A: The geometric sequence is given by -9, 27,-81,········ To evaluate : The 12th term in the geometric…

Q: Caroline saves money in an arithmetic sequence: $250 the first year, another $450 the second, and so…

A: Given :  Caroline saves money in an arithmetic sequence First year = 260 ; Second year = 450 and…

Q: The 15th term of an arithmetic sequence is 21 and the common difference is -4. (a) Find the first…

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Q: What is the value of the 23rd term of the arithmetic sequence -5, -9, -13, -17, -21,...? a23

A: The objective is to find the value of 23rd term of the given arithmetic sequence

Q: Write an expression that gives the requested term. The 11th term of the geometric sequence with…

A: Answer:

Q: The sixth and eighth terms of an arithmetic sequence are -12 and -22. Find the fifteenth term. a15

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Q: Find the indicated term of the arithmetic sequence with the given description.  The first term is…

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Q: Write an expression that gives the requested term. The 11th term of the geometric sequence with…

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Q: The first three terms of an arithmetic sequence are 7, 10.5, 14. a. What is the 31st term of the…

A: We have to find: a 31st term of the sequence b sum of first 31 terms of the sequence Where three…

Q: The first term is 25, and the common difference is 19. Which term of the sequence is 671?

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Q: The first three terms of an arithmetic sequence are 7, 10.5, 14. A) What is the 31st term of the…

A: The terms of the AP are, a1=7a2=10.5a3=14   The common difference is, d=a2-a1=10.5-7=3.5   Thus, the…

Q: When finding the nth term in an arithmetic sequence, how do I solve a sequence with fractions? For…

A: To justify that the seventh term of the given arithmetic sequence is 72/5 (given)

Q: rite a rule for the n​ th term of the geometric sequence. Then identify the first six terms o

A: Here we have fifth term of G.P = a5=162 The common ratio r=-3 Let first term =a

Q: 4 Find the sum of the first 3 terms of a geometric sequence with a = 18 and r= 3 The sum is

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Q: Find the 75th term of the arithmetic sequence with first term 2 and common difference -1/2.

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Q: Find the sum of the first 30 terms of the arithmetic sequence: 7, 3, -1, -5, . .

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Q: The 12th term of an arithmetic sequence is 34 and the fifth term is 20. Find the 20th term.

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Q: 12. Given that the 5th and 11th terms of an Arithmetic Sequence are 26 and -16, respectively,…

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Q: Write an expression that gives the requested term. The 11th term of the geometric sequence with…

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Q: Find the sum of the first 50 terms of the arithmetic sequence below. - 19, - 15, - 11, -7, .. The…

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Q: In an arithmetic sequence, the first term is -8 and the sum of the first 20 terms is 790 Whats the…

A: By using sum of arithmetic sequence formula, we calculate the common difference of arithmetic…

Q: 3) Find the sum of the first 12 terms of the geometric sequence-3,-6,-12,-24,..

A: We can solve as follows

Q: ind the 14th term of the geometric sequence 10, 40, 160,

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Q: The first term of an arithmetic sequence is 9, the last term is -39 and the sum is -195. Find the…

A: Given that: 1st term of AP, a=9Last term, l=-39Sum, S=-195

Q: The fourth term of an arithmetic sequence is 14, and the 20th term is 110. Find the common…

A: As we know that the nth term of the arithmetic sequence is: tn=a+(n-1)d Where 'a' is the first term…

Q: The 7th term of an arithmetic sequence is −44, and the common difference is −4. Find the first term.

A: The nth term of sequence is given by:…

Q: 5. The first term of an arithmetic sequence is 12, the last term is 120 and sum of the terms of the…

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Q: and common difference, d. Write the first six terms of the arithmetic sequence with the given first…

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Q: Write an explicit formula for the nth term of the arithmetic sequence. Find the sixth and tenth…

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Q: Which explicit formula describes the geometric sequence {,,7 }? ) an= + (n-1)(좋) (중)까-1 n-1 an =…

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Q: The first term of a geometric sequence is 15, and the 5th term of the sequence is 243 What are the…

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Q: An arithmetic sequence has a 10th term of 15 and 14th term of 35. a. What is the common difference?…

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Q: 1. Find the 25th term of the arithmetic sequence -7,-4, -1, 2, ..

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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.