Given two terms in an arithmetic sequence, find the first term and the nth term 4) a, = 30 and a, 106 30 11

Q: Given the arithmetic sequence 6,-1,-8,-15,-22. Find the 25 term

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Q: For a given arithmetic sequence, the 37 term, a7, is equal to 234, and the 73 term, a-, is equal to…

A: a37=234  &  a73=450⇒a+36d=234   →1  &  a+72d=450   →2    ∵an=a+n-1d Subtracting equation (1)…

Q: Given a geometric sequence with a 3= 20 and a 8= 640, find a 1 and r

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Q: Given Arithmetic Sequence a1, a2,·*, ɑn the first term is 25 and the common difference is 3, find…

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Q: In an arithmetic sequence (a1, a2, a3, the first term is 5 and the 15th term is 61, then S15 is 555…

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Q: in an arithmetic sequence, the first term, a1, is equal to 1, and the seventh term, a7, is equal to…

A: The nth term of an arithmetic sequence is given by an = a1 + (n – 1)d where a1 is the first term and…

Q: Find the 6th term of a geometric sequence is the first term is 2 and the common ratio is 3 a6=

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Q: In an arithmetic sequence , if a2 = –15 and az -34 , then the common difference d is %3D O 21 O -53…

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Q: In an arithmetic sequence , if a, = -11 and az = -26 , then the common difference d is -18 O 17 O 15…

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Q: The first three terms of an arithmetic sequence are given. Find an expression for t in n terms of n,…

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Q: If an arithmetic sequence has terms as = 20 and ag = 36, what is a15? 50 O 56 O 60 O 80

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Q: Given two terms of a geometric sequence, find the common ratio. a2 = 10 and as 250 O 12.5 0 5 120 O…

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Q: Given the arithmetic sequence an with aj = -7 and d = -9, find a3. ||

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Q: Find the nth term, the fifth term, and the tenth term of the arithmetic sequence.16, 13, 10, 7,…

A: Given: 16, 13, 10, 7,...

Q: The given pattern continues. Write down the nth term of the sequence {an} suggested by the pattern.…

A: Consider the given pattern. 4,-8, 12, -16,...  It is an alternating sequence having negative even…

Q: In a geometric sequence, the second term is 1 and the sixth term is 16, Find the common ratio and…

A: We have 2nd and  6th term are 1 and 16 respectively,  We have to find common ratio (r) and a15…

Q: Find the 9th, 24th, and nth terms of the arithmetic sequence. 3, 1, -1, ... ag = a24 = %3D %3D

A: First find the common difference of the given arithmetic sequence than use the formula to find other…

Q: Write an expression for the apparent nth term a n for the sequence. 10, −30, 90, −270, …

A: Given,The sequence -10, 30, -90, 270,…

Q: D. Given the specified terms of geometric sequence, find the first term and the common ratio, 1. az…

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Q: ind the formula for the nth term of the arithmetic sequence. 9,7,5, .

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Q: For a given arithmetic sequence, the common difference, d, is equal to 7, and the 41st term, 941…

A: NOTE: Refresh your page if you can't see any equations. . here we have the 41st term of the…

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

A: A sequence is funfction  from the set of natural numbers to the set of real numbers. A sequennce can…

Q: Given the explicit formula for an arithmetic sequence find the common difference, the first five…

A: Topic- sequence and series

Q: Show that the given sequence is arithmetic, and find the common difference.-6, -2, 2, . . . , 4n -…

A: An arithmetic progression is a sequence of numbers that has a first term and every succeeding term…

Q: The sixth term of a geometric sequence is 1215 and the third term is 45. Find the first term and the…

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Q: In an arithmetic sequence { 298, 281, 264, · . .... }, the common difference is. O -20 O 17 O 19 O…

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Q: Given a term in an arithmetic sequence and the common difference find the 52nd term and the explicit…

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Q: Use the formula for the sum of the first n terms of a geometric sequence to:Find the sum of the…

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Q: The given pattern continues. Write down the nth term of the sequence {a,} suggested by the pattern.…

A: 3, -6, 9, -12, .... From this series we see that each term is a multiple of 3. In fact the nth term…

Q: a = 5, a,+1=-3a,

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Q: For a given arithmetic sequence, the 29 term, a,o, is equal to 243, and the 89" term, ago, is equal…

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Q: Given the geometric sequence: 40 4, aj = 11 400 ao a2 = 121 find a formula for the n-th term:

A: The given geometric series is,a0=4,a1=4011,a2=400121,.....

Q: Given the first four terms in an arithmetic sequence, find the recursive formula. 39, 34, 29, 24

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Q: In an arithmetic sequence the ratio of the third to the eight term is 6:1 and the sum of the third…

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Q: Show that the given sequence is arithmetic, and find the common difference.53, 48, 43, . . . , 58 -…

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Q: Given an arithmetic sequence with a15 = 86 and a37 = 240, find the 104th term.

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Q: Given the sum of the first 6 terms of a geometric sequence is 27,342 and the common ratio is 5,…

A: Sum of first 6 terms of a geometric sequence is 27342 and common ratio is 5 we have to determine the…

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: Given the arithmetic sequence an with a1 = -10 and d = -2, find ag. Provide your answer below: az =

A: Given a1= -10 , d= -2 and n=3

Q: Find the common ratio and write out the first four terms of the geometric sequence (1.03)" n-1…

A: The nth term of the geometric sequence is given by an = 1.03n-1…

Q: Use the formula for the sum of the first n terms of a geometric sequence to:Find the sum of the…

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Q: Given the geometric sequence, find the value of r and a12. -1, 3, -9, 27, .. Or = -3 a12 = 177147…

A: We can find the correct answer in the following steps.

Q: The first three terms of an arithmetic sequence are given. Find an expression for t in terms of n,…

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Q: For a given arithmetic sequence, the first term, a₁, is equal to 21, and the 86th term, 96, is equal…

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Q: In a geometric sequence, a, = - 18, as = 2/3, find a6.

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Q: In the arithmetic sequence 7,23/3,25/3,…, which term is 51?

A: The given arithmetic sequence is 7, 233,253 where  first term a = 7              common difference d…

Q: Write an explicit formula for a_nan​, the n^{\text{th}}nth term of the sequence 180, -30, 5,

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Q: Use the formula for the sum of the first n terms of a geometric sequence to find the sum of the…

A: Given that the geometric sequence is 7,14,28,56,112,....

Q: The first four terms of an arithmetic sequence are given by a1 = 6, a2 = 12, az = 18, and a4 = 24.

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Q: The tenth term of an arithmetic sequence is 32, and the fifth term is 16. Find a, d, and the 20th…

A: Given: The tenth term of the arithmetic sequence is 32. The fifth term of the arithmetic sequence is…

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.