Consider an arithmetic sequence with the first term ai = 300 and common difference d = -90 Use the formula for the general term, an to find a20. What does the term "common difference" mean? Explain in detail.

Q: The 12th term of an arithmetic sequence is 59, and the fifth term is 31, Find the 20th term. 820 =

A: Topic = Sequence

Q: The 3rd and 4th terms of an arithmetic sequence are 13 and 18, respectively. What is the 50th term…

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Q: Write a recursive formula for finding the nth term of each arithmetic sequence. 15.75, 14.25, 12.75,…

A: First Term of the sequence is a1=15.75 common difference is: d=an-an-1=a2-a1=14.25-15.75=-1.5…

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

A: Term formula of geometric series is Where an= n_th term r=common ratio

Q: Find the common difference and the sum of the first 5 terms of the arithmetic sequence. an = 5n – 2

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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: The 20th term of an arithmetic sequence is 96, and the common difference is 5. Find the nth term.

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Q: How many terms are in the geometric sequence   15,  30, …, 15360 ?

A: Given  geometric sequence 15,30, ---------,15360 Where a1= first term =15               R = common…

Q: Write the arithmetic sequence – 4, – 13, – 22, – 31, .. in the standard form: an

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Q: Write the arithmetic sequence 38, 34, 30, 26, ... in the standard form: an

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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 the arithmetic sequence 15, 17, 19, 21, ... in the standard form: An

A: here the first term is  . find the common difference

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: 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: An arithmetic sequence is given below. 10, 3, -4, -11, th term d, Write an explicit formula for the…

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Q: Determine the value of the 100th term of the arithmetic sequence 130,123,116,109. Give the answer…

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Q: Exercise 4. If the 1st and 15th terms an'arithmetic sequence are -5 and 23, respectively, find the…

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Q: Find the 8th term of the geometric sequence 6, 18, 54, ...

A: A sequence is a function with domain being the set of natural numbers and the range being the set of…

Q: Write a formula for the general term the nth term of the arithmetic sequence:-4, 2, 8, 14, . . . .

A: we have to write  a formula for the general term the nth term of the arithmetic sequence:-4, 2, 8,…

Q: Write the arithmetic sequence 37, 29, 21, 13, .. in the standard form:

A: Arithmetic series: An=A0+(n-1)d

Q: Write the arithmetic sequence 38,35,32,29,... in the standard form: an=

A: Given sequence  38,35,32,29.....  To find  nth term of given sequence

Q: Which explicit formula describes the arithmetic sequence {19,14,9,4,...}

A: The arithmetic sequence is given by 19, 14, 9, 4, ····· To determine : The explicit formula of the…

Q: In the arithmetic sequence 7,233,253,…, which term is 51?

A: The given arithmetic sequence is 7, 233, 253 ............................ Where  first term a = 7…

Q: Find the 12th term of the geometric sequence 7, –35, 175, ...

A: Solving the problem by obtaining the 12th term of the sequence.

Q: Write the arithmetic sequence – 14, – 17, – 20, – 23, ... in the standard form: An

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Q: Write an expression for the sum of the first n terms of a geometric sequence.

A: Given data:   The given number of terms in the geometric sequence is: n.   The expression for the n…

Q: The second and fifth terms of a geometric  sequence are 30 and 3750, respectively. Which term of the…

A: nth term of a geometric sequence is given by- an=arn-1 Where a is the first term and r is the common…

Q: The middle term of an arithmetic sequence equals 17, the last term = 32, and the fourth term = 11.…

A: Given middle term = 17 Last term = 32 Fourth term = 11 T4 = a+3d = 11 Middle term = T6 = a+5d = 17…

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: Find the fifth term of the geometric sequence from the given information. Express the term as an…

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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: The 5th term of an arithmetic sequence is 47 and the 17th term is 152. Find the first term and…

A: general term of arithmetic sequence  an=a+(n-1)d .........(1)where a=first term and     d=common…

Q: The sixth term of an arithmetic sequence is 28 and the ninth term is 36.Calculate the sum of the…

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Q: Find the 13th term of the geometric sequence 6, – 30, 150, ...

A: The first term is, a1 = 6  &, The common ratio is, r = - 5

Q: Which arithmetic sequence has a common difference of -21? O (1,563; 1,587; 1,611; 1,635;...) (32,…

A: Common difference means subtraction of second term and first term

Q: The second term of an arithmetic sequence is 24 and the fifth term is 3. Find the common difference.

A: The second term of an arithmetic sequence is 24 and the fifth term is 3. Find the common difference.

Q: The 7th term of an arithmetic sequence is −41, and the common difference is −2. Find the first term.

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

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Q: 85. If the common For an arithmetic sequence, a21 = difference is -3, find: ai = the sum of the…

A: To find the a1 and S36.

Q: Write the arithmetic sequence – 5, – 8, – 11, – 14, ... in the standard form: - - an

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Q: 44. Make Sense and Persevere After the first raffle drawing, 497 tickets remain. After the second…

A: Given: After first drawing, 497 tickets remains. And, after second 494 tickets remans. As, the…

Q: Find the common ratio of the geometric sequence: {- 3, 21, 147, 1029, – 7203, ...} | r = Submit…

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Q: An arithmetic sequence has the 5th term equal to -64 and the 14th term equal to -1. Calculate the…

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Q: An arithmetic sequence has a first term of 0 and a 9th term of 12. Which term number corresponds to…

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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: Write the arithmetic sequence – 5, 2, 9, 16, ... in the standard form: an

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Q: The fourth term of an arithmetic sequence is 11, and the sixth term is 17. Find the second term.

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Q: Write the arithmetic sequence 6, 9, 12, 15, ... in the standard form: An

A: Here I am attaching image so that you understand each and every step.

Q: Write the arithmetic sequence – 11, – 3, 5, 13, ... in the standard form: an

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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.