III. SHOW ALL NECESSARY SOLUTIONS NEATLY AND ORDERLY 1. Given the nth term of the geometric sequence: a, = (-4)(-5" a. Generate the first four terms b. Find the sum of the series if it exists as n goes to infinity. 2. Find the fifth term of the geometric sequence if its 3 term is -486 and its 8 term is 2.

Q: A. Write the first four terms of the geometric sequence in which a, and r are as follows: 1. a, =7,…

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Q: 3. Find to given two terms in a geometric sequence, t₁ = 192 and t₂ = 49,152. [5]

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Q: Write the first five terms of each of the following Geometric Sequence. 1. an = 2(3)n 2. an 6(-2)" =…

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Q: Find a formula for an for the arithmetic sequence. a1 = 0, d=- a. 4 аn - Эл - 5 b. an An=-31+3 d. 4…

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Q: 4. What is the fourth term in the sequence defined as: a1 126 and an 3(an-1) - 5 %3D %3D

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

Q: Find the first three terms of the sequence whose nth term is as follows:

A: A sequence is a set of numbers that has a particular order or obeys a general form. The nth term of…

Q: 4. In an arithmetic sequence, t₁0-11 and t18=27, determine the first 2 terms.

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Q: Lakeisha wants to put down new tile in her home. The tile costs $3.50/ft2 and labor is $4.00/ft2.…

A: Given,           Lakeisha wants to put down new tile in her home. The tile costs $3.50/ft2 and…

Q: Find the nth term of the arithmetic sequence with the first term −2, common difference 3, and n =…

A: Given: The first term =-2 Common difference =3 n=10 To determine: nth term of the sequence.

Q: Find the sum of the first 4 terms of a geometric sequence with a = 270 and r= The sum is 2/3

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Q: Find the sum of the first 6 terms of the given geometric series: -2-4-8-16.. O -146 -139 O 2 O -126

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Q: Match the terms on the left with the formulas on the right. nth term of an arithmetic sequence nth…

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Q: What is the explicit formula for the sequence if at 8 am a hospital patient has 100 mg of a…

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Q: 50. Find all values of x such that x – 7,x + 7, and 4x – 7 form a geometric sequence. 32 A. x = 0 or…

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Q: Find the 10th term of the arithmetic sequence in which a1=12 and d = 9.1.

A: It is given that, a1=12d=9.1   It is known that nth term of arithmetic sequence can be found  by…

Q: 12. Find the first 5 terms of the sequence: 2n a, =(-1)" n +1 a) b) a, = 4a-5 and aj =1 | n-1

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Q: Write the first 5 terms of each sequence a(1)=7,a(n)=a(n-1)-3 for n>2. 2. B(1)=2,b(n)=2•b(n-1)-1…

A: we have given relation in sequence.  We have to find the first 5 terms of the sequence

Q: 3. Find t10 given two terms in a geometric sequence, t5 = 1875 and t, = 46875. %3D %3D

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Q: 3. Find a formula for the sequence given by In+1 = Xn+ 8xn-1 – 12xn-2 n > 2, with ro = -4, 1 = -3…

A: Let 2nd order homogeneous difference equation is given by,…

Q: B. Give the next three terms for each geometric sequence. 1. 2, 6,. 2. 0.1, 0.3, 0.9,0.27.. 3. 100,…

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Q: Find a n for the geometric sequence a 1 =-4; r = - 2, n = 10

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Q: Find these terms of the sequence {a}, where a 2.(-3)" + 5". a. a b. a₁ c. a What is a of the…

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Q: 5. a1 = 2, an+1 = = 2a-3

A: To calculate the first four terms of the sequence, starting with n=1. a1=2, an+1=2an2-3

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.