Given that the 8th and 15th terms of an arithmetic sequence are 25/2 and 2, respectively, then the first term of the sequence is Note: DO NOT use a comma and space bar, express your answer in fraction in lowest terms, if applicable

Q: Find the explicit formula for the given sequence. 2, 8, 32, 128, ....​

A: SOLUTION-

Q: In an arithmetic sequence, if az = -12 and ag =-31, then the common difference d is O 19 O 22 O 21 O…

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Q: For the geometric sequence (4, 16, 64, 256, - - , the term a17 O 416 O4.416 O 4.43 O4.418 O4.45

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Q: For a sequence with a first term of 5 and a common ratio of 4, what is the 11th term?

A: For the given sequence,  First term, a = 5 Common ratio, r = 4 11th term, a11 = ? So, n = 7

Q: Find the explicit formula for the arithmetic sequence Cn given below - note that c1=−4.…

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Q: Given the recursive rule for an arithmetic sequence, write the explicit rule. 5. f(1) = 19 and f(n)…

A: Question number 5,Given,          f1=19 and fn=fn-1-10 for n≥2

Q: Given that the 8th and 15th terms of an arithmetic sequence are 25/2 and 2, respectively, if the nth…

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Q: Find the first term of an arithmetic sequence if the 9th term is 72 and the common difference is 5.…

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Q: 1. What is the 5th term of the geometric sequence described by a, = 5(1.5)"? %3D O az = 5.0625 %3D O…

A: The given question can be solved as shown in step2

Q: Given a sequence defined by the explicit definition: tn = 2" – n, find the 5th term of the sequence.…

A: It is given that,the sequence:tn=2n-n We have to find the 5th term of the sequence.

Q: Determine the common ratio r, the fifth term, and the nth term of the geometric sequence. 2, 2° + 1,…

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Q: Show that the given sequence is geometric, and find the common ratio.

A: Explanation: A geometric progression is a sequence of non-zero terms in which ratio of any term and…

Q: Identify the explicit formula for the nth term of the sequence written below.   10, −50, 1000/3,…

A: The explicit formula is the formula that can give any term of the sequence upon inserting the…

Q: Find the explicit formula for the given sequence. 2, 8, 32, 128, ....

A: TO find the explicit formula of given sequence .first check the common ratio terms since ratio is…

Q: The first three terms of an arithmetic sequence are as follows. 31, 24, 17 Find the next two terms…

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Q: The nth term of a sequence, represented by an, is called the______ term.

A: Given, The nth term of a sequence, represented by an

Q: For a given geometric sequence, the common ratio, r, is equal to 5, and the 12th term, a₁2, Is equal…

A: The nth term of a geometric sequence is given by  an = a1·rn-1 where a1 is the first term and r is…

Q: The non-recursively defined formula for writing an arithmetic sequence is given by: an = C+ (n -…

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Q: Consider the following sequence 4/7, 9/14, 5/7, 11/14, ____, if arithmetic, give d. and supply…

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Q: The first three terms of an arithmetic sequence are as follows. 15, 23, 31 Find the next two terms…

A: Arithmetic Progression is sequence of numbers where any two consecutive number has same difference.…

Q: Given that a is an arithmetic sequence, a1=6 and a10=60, what is a21?

A: Given arithmetic sequence in which we have a1=6 and a10=60. To find: a21 Solution: In arithmetic…

Q: Given that a is a geometric sequence and az = and a5 what is a12?

A: Let the first term is = a and common ratio=r Given that

Q: The following sequence is geometric: -1, 1, -, . O True O False

A: Given the geometric sequence−1,12,14,−18

Q: Determine the common ratio r, the fifth term, and the nth term of the geometric sequence. 1, V3, 3,…

A: Given : 1,3,3,33,.........

Q: Suppose that a sequence is defined as follows. a1=-2, for n>2 an= 3a,-1+2 List the first four terms…

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Q: 2" An 2n+1

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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: For a given geometric sequence, the common ratio, r, is equal to 2, and the 10th term, ₁o, is equal…

A: Here, nth of a GP , an = a1 × r(n - 1)

Q: The following sequence is geometric: -3, 9, -27, 81, ... O True O False

A: Please refer the attached image for complete solution. THANK YOU.

Q: Identify the explicit formula for the nth term of the sequence written below.   14, -98,2744/3,…

A: 14,-98,27443, -9604, 537824/5, -3764768/3

Q: Given that the first term of an arithmetic sequence is 50 and the common difference is -5, what is…

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Q: For a given geometric sequence, the 1st term, a₁, is equal to 11 9 your answer as a fraction. and…

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Q: Given the following sequence, provide the (unsimplified) sum of the first 14 terms: -6, 12,-24, 48,…

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Q: Is the following sequence arithmetic, geometric or neither? 2, 10, 50, 250, 1250, 6250

A: Given,         The sequence is 2 , 10 , 50 , 250 , 1250 , 6250 .

Q: For the geometric sequence {4, 16, 64, 256, - . . .. -}, the term a17 O 4.418 O 4.45 O 4.43 4 - 416…

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Q: Use the formula for the sum of a geometric sequence to write the following sum in closed form. 4 +…

A: The given sum is 4+42+43+⋯+4n where n is any integer with n≥1. Express the following sum in closed…

Q: What is the 11th term of the arithmetic sequence 1+2i, 3+3i, 5+4i...

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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: Find the nth term to illustrate the given arithmetic sequence. 4,9 14, 19, 24,29... 15, 0, -15, -30,…

A: 2) Given sequence is 15, 0, -15, -30, -45, ... Here a=15, d=-15 The nth term formula is,…

Q: Given that the 8th and 15th terms of an arithmetic sequence are 25/2 and 2, respectively, if the nth…

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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: If the sequence 1, 0.3, 0.09, 0.027 is a geometric sequence, find the sum of the first five terms.

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Q: Is the following sequence arithmetic, geometric or neither? 15, 60, 240, 960, 3840, 15360

A: Given,          The sequence is 15 , 60 , 240 , 960 , 3840 , 15360.

Q: For a given geometric sequence, the 4 41 term, a, is equal to , and the 9th 625 term, ao, is equal…

A: Given Data: The 4th term of the geometric sequence is: a4=41625 The 9th term of the geometric…

Q: What are the first three terms of the sequence given that the nth-term formula is an=n/(n+1).

A: Given, nth-term of sequence is an=nn+1  find first three terms of the sequence-

Q: For the geometric sequence (9, 54, 324, 1944, }, the term a17 =. O 6-68 616 6-610 O 9.616 O 9.618

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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: Let be the arithmetic sequence defined by the formula a = 11 + (n-1) × 6 Apply the concepts of the…

A: Given tn= 11 + (n-1) × 6 Compare with tn= a+ (n-1) d⇒a=11,d=6

Q: find the explicit formula for the general nth term of the geometric sequence…

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Q: For Exercise, write the first five terms of the sequence defined recursively. di = 30; d, = d,- - 1

A: We plug n=2 in the given formula and d1=30