The product of the third and the sixth terms of an arithmetic sequence is 406. The ninth term of the sequence divided by the fourth term gives a quotient of 2 and a remainder of 6.Find the first term and the common difference of the arithmetic sequence

Q: What would be the easy way to figure out the 100th and nth of the sequence:  1, 4, 9, 16, 25, 36,.

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Q: The first term of an arithmetic sequence is equal to 6 and the common difference is equal to 3. Find…

A: The first term of the arithmetic sequence, a1 =6 he common difference,d= 3

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A: 9, 18, 27, 36, ........ It is an arithmetic sequence with, First term=a=9Common difference=d=9

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A: Find the common difference, d:

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A: Please refer to the image below

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Q: If the fourth term of an arithmetic sequence is 13 and the second term is 3, find the 24th term.

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Q: m of the first 10 terms in an arithmetic

A: Given, the sum of the first 10 terms in an arithmetic sequence is 530.

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A: We have the given expression as 4+(0.1)n   We have to find   First four terms and eight term

Q: For a given arithmetic sequence, the  11th  term,  a11 , is equal to  −49 , and the  38th  term,…

A: Consider the following formula: an=a+n-1dhere,first term=adifference between two consecutive term=d…

Q: The sum of two consecutive terms in the arithmetic sequence 1​, 4​, 7​, 10​, ... is 299​; find these…

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Q: Find the 37th term of an arithmetic sequence whose second and third terms are −4 and 12.

A: Note:-  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: For a given arithmetic sequence, the first term,  a1 , is equal to  11 , and the  36th  term,…

A: The n-th term of an arithmetic sequence with first term a1 and common difference d, is given by, an…

Q: The 7th term of an arithmetic sequence is −44, and the common difference is −2. Find the first term.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: The third term of a sequence is 64 while the seventh term is 4. Determine the sum of the first ten…

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Q: Find the first six terms of the sequence. a1 = -3, an = an-1 + 8 %3D

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Q: is equal to 240, and the 5" term, ac, is equal to 36. a73 term, For a given arithmetic sequence, the…

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Q: For a given arithmetic sequence, the 39th term, a39, is equal to 265, and the 76th term, a76, is…

A: topic- arithmetic sequene

Q: given arithmetic sequence, the 6th term, a6 , is equal to −39 , and the 37th term, a37 , is…

A: Concept:

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Q: If the third term of an arithmetic sequence is 4 and the seventeenth term is -66​, find eighth the…

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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 the sum of the first 23 terms of the arithmetic sequence 4m – 3, –10, .

A: For the terms to be in an AP , the first term should be 4 and not 4m which is a mistake.

Q: Find the first term, a1, and the common difference, d, of the sequence. 13, 10, 7, 4, 1, ...

A: The given sequence is 13, 10, 7, 4, 1,.... So the first term is=a1= 13

Q: Write the first four terms of the sequence whose nth term, or general term, is given: an = 3n + 4

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Q: Find the nth term of a sequence whose first several terms are given. 3, 16' 25 an

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Q: For a given arithmetic sequence, the common difference,  d , is equal to  −4 , and the  3rd…

A: Given data set: Common difference = d = -4 Third term (a3) = 21   We need to calculate the value of…

Q: The tenth term of an arithmetic sequence is 40 and the twentieth term is 30. Find the common…

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Q: If the common difference of an arithmetic sequence is 4 and a(6 ) = 15, find the first term of the…

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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: find a formula for the nth term of the sequence. 2, 6, 10, 14, 18,...

A: 2, 6, 10, 14, 18,........ It is an arithmetic sequence with

Q: The first term of an arithmetic sequence is equal to 200 and the common difference is equal to -10.…

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Q: Find a formula for the nth term of the sequence 1, - 4, 9, – 16, 25, ..

A: We can find the nth term of the sequence. We notice pattern of the sequence.

Q: Find the first four terms and the eighth term of the sequence.

A: The given sequence is 2+-0.1n.

Q: The fifth term of an arithmetic sequence is 24, and the sum of the first 10 terms is 265. Write the…

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Q: Write the formula for the nth term of the sequence: 2, 5, 8, 11, ...

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Q: The sum of the first 10 terms of an arithmetic sequence is 530. What is the first term if the last…

A: I have appended the formula used in the solution part.

Q: Find the nth term of a sequence 2,5,10,17,26, ...

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Q: (2п)! An

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Q: Please answer the 3 questions with solution 6. If 5x + 2, 2x^2 +8, 24x - x^2,...form an arithmetic…

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Q: If the numbers r, z+1, 2(z +3) are consecutive terms of a geometric sequence, what is the value of…

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Q: If the fifth term of a geometric sequence is 64/27 and the sixth term is 256/81 , find the sum of…

A: Let the G.P. is a, ar, ar2, ar3, . . .arn-1 Sum of first n terms is given by, Sn=a(rn-1)r-1, r>1…

Q: Find the 22" term of the arithmetic sequence whose common difference is d=2 and whose first term is…

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A: Topic - arithmetic progression

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Q: Find the next term of the sequence: 4, 20, 100, 500, 2500,

A: Given To evaluate next term of series

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.