1. Express the geometric sequence as an explicit formula. Then find the 20th term. Sequence: 1, 3, 9, 27, ... а. а, 3D 1 b. r = 3 c. f(n) = 1 • ( 3)(n-1) d. f(20) = 1 • ( 3)20–1)

Q: 1. Write the first five terms of the sequence defined by i) a, = (-1)"+1 Li. ii) b, = . 2. Find a…

A: Given: Question 1(i)  an=(−1)n+11+nn!(ii)  bn=2nn!find five termsQuestion 2(i)…

Q: Find a formula for the general term a, of the sequence, assuming that the pattern of the first few…

A: We need to look the pattern of given sequence to find general solution

Q: Which explicit formula describes the geometric sequence {1/3,1/9,1/27, 1/81…}? A. an= 1/3 (3)^n-1…

A: Given sequence is: 13,19,127,181, ...

Q: Find the partial sum Sn of the geometric sequence that satisfies the given conditions. a = 8, r = 2,…

A: Given: a=8, r=2, n=6

Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

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Q: Select the first five terms of the sequence. (Assume that n begins with 1.) an = (-1y"| n+11

A: Substitute n = 1 and 2  and then find a1 and a2.

Q: 1. Find these terms of the sequence (a,), where a, = 2 (-3y"+5". %3D b) a c) as d) as a) do

A: .

Q: Find a formula for the general term a, of the sequence, assuming that the pattern of the first few…

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Q: 1. The general formula for a sequence is t = 3t₁ - ₁ - n, where t₁ = 3 Find the fourth term.

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Q: th Find the 10 term of the following geometric sequence. 2, 8, 32, 128,

A: We have to solve the above GP

Q: 13. Solve for x & y if the given sequence is arithmetic 2х + 5y, 2y, 3х + 2, 4x — Зу

A: Given- 2x+5y,2y,3x+2,4x-3y To Find- The value of x and y if the above sequence is arithmetic.

Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

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Q: (a) A town has a population of 5000 persons, but is expected to grow by 2% every yea (1) What would…

A: Given, Initial population of a town is 5000 persons. It is given that it increases at a rate of 2%…

Q: Find a formula for the general term a n of the sequence, assuming that the pattern of the first few…

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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: Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common…

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Q: 3. What is the 10th term of the sequence whose nth term is an = (n^2+2n-3)/(n+1) ? * O 117/11 O…

A: We are given the nth term of the sequence and we need to find the tenth term of the same. This can…

Q: 14. Which explicit formula describes the geometric sequence {, ,7 8T}? 1 1 O an = (3)"-1 O + (n –…

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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 a formula for the nth term of the sequence where an is calculated directly from n. 5/1 , 7/2 ,…

A: The detailed solution is given below Thank you

Q: Use iteration to guess an explicit formula for the sequence defined by an = an-1 + n for all…

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Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

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Q: Find a formula for the general term a of the sequence, assuming that the pattern of the first few…

A: The given sequence has first term a1 =-2 and ratio, r = -2/3   Therefore,  it will follow…

Q: Find an explicit formula for a sequence of the form a,, az, a3 with the initial terms given below.…

A: To find  An explicit formula for a sequence of the form with the given initial terms.

Q: A geometric sequence has the third term 2 and seventh term 0.125. Express it as a direct formula.…

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Q: The repeating decimal 0.555 can be represented as the sum of a geometric sequence where a is the…

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Q: 1. Give the first five terms of the sequence with the given general term. a. a, = 3n+4 %3D b. а,…

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Q: B. Find the first three terms of each sequence using the given rule. 1. a = 2 and an= an-1+3, for…

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Q: 3,16

A: Answer is below

Q: Find a formula for the nth term of the sequence in terms of n. 2 22 23 24 15 20' 25 30' 35 1 an for…

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Q: Given that the first term of an geometric sequence is 2 and the common ratio is 3 what is the…

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Q: Find the partial sum Sn of the geometric sequence that satisfies the given conditions. a = 7, r = 2,…

A: Given that first term a=7, common ratio = 2 , number of terms n=5   Then we will use the sum formula…

Q: Find a formula for the nth term of the recursively defined sequence where a, =1, an+1 an for n21. 4"

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Q: Find the formula an for the n th conditions: a₁ = term of the geometric sequence satisfying the…

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Q: 2. Given that a10 = 78 and a25 = 198 are terms of an arithmetic sequence, find an. 3. 6, 10, 16,…

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Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

A: Given the sequence is { 1, 1/3, 1/5, 1/7, 1/9,..............} Given that the 'n' starts with '1'

Q: 6. Write an nth term (general term) of the geometric sequence that has the given two terms: a. t, =…

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Q: Determine the first four terms of the arithmetic sequence represented by the explicit formula an =…

A: Given, an=7(n-1)+8Here we consider n>0

Q: 1. Consider the sequence defined by the explicit formula AN = N² +1. a) Find A₁ = b) Find A100 = c)…

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Q: = (-1)"/(n³). Write the first five terms of the sequence whose nth term is a, a, = a2 az = as

A: Solution is given below:

Q: Given the arithmetic sequence of 4, 2, 0, -2, . .fund an explicit rule for the nth term. O an = an 1…

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Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

A: Consider the sequence

Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

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Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

A: Given the series -5,103,-209,4027,-8081,..... To find : The formula for general term an of the…

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: 7. Find the first five terms of the sequence defined by each of these recurre a) an = 6an-1, a0 = 2…

A: Introduction: A recurrence relation is a formula that describes a series based on a rule that…

Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

A: Given sequence 6,13,20,27,34,.... First term of the sequence is  a1=6 Common difference  d=an-an-1…

Q: Find the n th term a of a sequence whose first four terms are given. 5 6. 7 8 - ... 11 22 33 44'

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Q: Write a recursive rule for the geometric sequence shown on the graph. 7. 200 fn), 8. 10 (1, 10) 160…

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Q: Find a formula for the general term a, of the sequence, assuming that the pattern of the first few…

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