For the following sequence, give an explicit formula for the nth term. aj = 6 %3| An -5a,-1 for n > 2

Q: For the following geometric sequence, find the recursive formula  {-80,20,-5,...}

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Q: For Exercise, find the sum of the geometric series, if possible. SU 10 Σ 3/2)1 n=1

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Q: Calculate the required term for the sequence with the following given: a1 = 4 , r=6 , a10 =?

A: If a, ar, ar2, ar3, ... are in geometric sequence with first term a1= a and common ratio r then the…

Q: For Exercise, find the indicated term of a geometric sequence from the given information. and r =…

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Q: Given the following sequence, provide the (unsimplified) sum of the first 16 terms: 4/5, 4, 20, 120,…

A: Given sequence is  4/5 , 4 , 20 , 120 Series is Geometric Progression Series has first term as 4/5…

Q: Find an explicit formula for the following sequence. 3 15 19 where n 1 - 1' 22 4 5

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Q: Find the common ratio, r, for the following geometric sequence. 3, 15, 75, .

A: Here, the common ratio r = 153 = 7515 = 5

Q: Find the first six terms of the following sequence. an = -2 – 7(-1)", for n > 1. %3D

A: To solve this problem we need to have an understanding about the powers of -1.

Q: se the formula for the sum of the first n terms of the geometric sequence, and then state the…

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Q: The domain of the following sequence ( where n is natural number *:) is /5-n n- 4

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Q: As n increases, the terms of the sequence:get closer and closer to the number e (where e ≈…

A: Substitute 10 for n in the expression to calculate the value of a10.

Q: Find the first four terms of the sequence given by the following. (-1)"*1 an п3D 1, 2, 3, ... %3D…

A: We have to find first four terms of the given sequence.

Q: For the following geometric sequence: find an. 1, 2, 4, 8, ...; find a13. a13 %3D

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Q: What is the sum of the sequence E(1+k!) R-0

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Q: Find a formula for the nth term of the sequence in terms of n. 3 32 33 34 1 10' 15' 20' 25' 30

A: We have to find the nth term of the sequence.

Q: For the following sequence, give an explicit formula for the nth term.…

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Q: Find the sum Sn of the arithmetic sequence that satisfies the stated conditions.a1 = 5, d = 0.1, n =…

A: Given:              a1 = 5, d=0.1, n=40 Formula to be used:              Sn = n22a1+(n-1)d Where,…

Q: Find a formula for the nth term of the sequence in terms of n. 1 2 22 23 24 9' 12' 15 18' 21 ** ...…

A: Try to observe the pattern in numerator and denominator separately.

Q: Find an explicit formula for the following sequence, an which starts with aı = -1. 1 11 1 3'7'5…

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Q: calculate the first four terms of the sequence, starting with n = 1. cn=3n/3!

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Q: Find the explicit formula for the geometric sequence C, with the following information given. c1 =…

A: Given: For the geometric sequence cn, we have c1 = 10, c4 = −80/27.

Q: Use the formula for the general term (the nth term) of a geometric sequence , to find the indicated…

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Q: Find the explicit formula for the geometric sequence c, With the following information given. C1 10…

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Q: Find an explicit formula an for the nth term of the geometric sequence whose first term is a, = 4…

A: Use general formula of geometric series

Q: For the following sequence, state the next three terms. 15, 45, 135, 405, 0 State a formula for the…

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Q: Find the twelfth terms of the sequence described by the explicit formula f(n) = 7 - 2( n-1) %3D…

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Q: Find the first five terms of the following sequence, starting with n = 1. b, = (-1)"(4n² – 4) Give…

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Q: For the following sequence, give an explicit formula for the nth term. a1=6 an=−5an−1 for n≥2

A: We have to find nth term

Q: Find the formula for the nth term of the sequence. 10

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Q: Use iteration to guess an explicit formula for the following sequence - dz = 5dr-1 + 3, for all…

A: Given dk = 5dk - 1 + 3, ...... (1) dk - 1 = 5dk - 2 + 3 ......(2)

Q: For Exercise, find the sum of the geometric series, if possible. ΣΘ. 00 Σ 18| n-1 3 n=4

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Q: For the following sequence, give an explicit formula for the nth term for n ≥ 2. an 2 a₁ = 2, an+1 =

A: We are asked to find the explicit formula for the sequence.

Q: Find the explicit formula for each of following sequence: а) -31, -14, 3, 20, 37, 54, b) 1/5, 1/25,…

A: Given: a)-31,-14,3,20,37,... b)1/5,1/25,1/125,1/625,... c)17,10,3,-4,-11,-18,.... As per our…

Q: For the following sequence, state the next three terms. 39, 34, 29, 24, The common difference is :…

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Q: For the following determine if the sequence is increasing, decreasing, not monotonic, bounded below,…

A: Given, 1-nenn=3∞ We know that, If given sequence an<an+1  for all n then the given sequence is…

Q: The sum, Sn, of the first n terms of the sequence is given by the formula Sn =______ , where a1 is…

A: The sum, Sn, of the first n terms of the sequence is given by the formula Sn = a1(1-rn)(1-r)

Q: Find the sum of the finite geometric series by using the formula for Sn 16 32

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Q: Find the first five terms of the following sequence, starting with n = = 1. a, = (-1)"+'(6n² – 1)…

A: Answer and explanation is given below..

Q: Use the formula for the general term (the nth term) of a geometric sequence , to find the indicated…

A: Given: a=4, r=-2 we know that nth termTn of a geometric progression is given by Tn=a.rn-1…

Q: Find the fifth terms of the sequence described by the explicit formula. f(n) = -9.2 -2.5( n-1) %3D…

A: Given function is f(n)=-9.2-2.5(n-1)

Q: Find a, and a, for the following geometric sequence. अ-4.r--3 a.

A: We write geometric sequence like this:                 a1, a1r, a1r2, a1r3, ..., a1rn-1,... where,…

Q: Use the formula for the general term (the nth term) of a geometric sequence to find the indicated…

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Q: Find a formula for the nth term of the sequence in terms of n. 1 2 22 23 24 20' 25' 30' 35' 40

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Q: Find a formula for the nth term of the sequence where a, is calculated directly from n. 37 11 15 19…

A: The numerators are 3, 7, 11, 15, 19,... This is an arithmetic progression with a common difference…

Q: For Exercise, find the nth term an of a sequence whose first four terms are given. 1· 2 1.2.3…

A: Let Tn be the nth term. Examine the numerator of T1 = 1.2; that of T2 = 1.2.3; that of T3 = 1.2.3.4…

Q: For the following sequence, state the next three terms. 12, 16, 20, 24, State a formula for the nth…

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Q: For the following items, consider the sequence {()"-}. 1. What are the first five terms of the…

A: We have to find 1st five point and draw the graph as well as the property of sequence

Q: For a given arithmetic sequence, the 95th term, 495, is equal to 786, and the 12th term, 4₁, is…

A: Given

Q: For Exercise, find the indicated term of a geometric sequence from the given information. and r = 64…

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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.