It is given that three positive integers form an arithmetic sequence. Find these three integers if a. their sum and their product are 15 and 80, respectively, b. their product is 11 times their sum. (Hint: Let the three integers be a-d, a and a + d.)

Q: If x + 1, 2x + 2 and 5x + 2 form a geometric sequence, find the value of the first term. O 4 O 2 O 5

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Q: Find the 20"" term of the arithmetic sequence whose common difference is d= 5 and whose first term…

A: The formula to find the nth term in arithmetic sequence is given below: an=a1+n-1d where, a1 is the…

Q: Find the sum to infinity of the geometric sequence. 1/3, 1/9, 1/27, 1/81, …

A: Given series is 13,19,127,181From here a1=13 and a2=19We know that r=a2a1=1913=13

Q: Find the indicated term of the geometric sequence. 2,6, 18, ...; a7

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

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

Q: Find these terms of the sequence (a where an=2-3)"5"

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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: Write the explicit form for the nth term of the following geometric sequence.  4,15,45,135…

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Q: For the given geometric sequence. Find the sum of the first 6 terms of 3, -6, 12, ….

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Q: is The common ratio for the geometric sequence %.4. 2. 1. O A) -2 O B) O C) 2 O D) -

A: The given geometric sequence is                                                     8 , 4 , 2 , 1 ,…

Q: Which explicit formula describes the geometric sequence { 1 1 1 3' 9 27 ' 81 .. n-1 an=+(n- 1) ()…

A: The given sequence is: 13,19,127,181,... That is: 13,132,133,134,... So, the general form of the…

Q: For Exercise, write the first five terms of the sequence defined recursively. 1 b1 = 10; b, = ba-1

A: Given sequence defined recursively as  Substituting n=2,3,4,5, we get

Q: If the general term of an arithmetic sequence is :- 1 2n. T(n) = %3D then the

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Q: Write out the sequence that can be described by the explicit definition: an n? + 2n ?

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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 what value of K will K, K-2, K-3 be in terms of geometric sequence?

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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: Find an and a- for the following geometric sequence. a, = - 4, r=2 -1 an a7 =

A: Given:          a2=-4           r=2 The nth of geometric sequence is calculated as…

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: 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: If a1, a2, a3, a4, ... is a geometric sequence with common ratio r, show that and determine the…

A: Given  is a geometric series with common ratio r, so we have

Q: Which of the following is a geometric sequence?

A: We know that,          A sequence is in geometric sequence when the common ratio between the…

Q: Find the sum to infinity of the geometric sequence given below 1. 12, 4. .. .... 2. 900, 9, 0.09,...…

A: 1): Hera1=12a2=4a3=34This is not a geometric progression as a1a2 and a2a3 are not equal.SO, it is…

Q: -For each sequence, decide whether it could be arithmetic, a. 25, 5, 1, ... b. 25, 19, 13, ... c. 4,…

A: Given: a)  25,  5,  1,  ...b)  25,  19,  13,  ...c)  4,  9,  16,  ...d)  50,  60,  70,  ...e)  12,…

Q: Write the first five terms of the geometric sequence whose first term is 2, and whose common ratio…

A: Given problem:- Write the first five terms of the geometric sequence whose first term is 2, and…

Q: If the expressions X+2, 3x-8, 4x+2 represent the first three terms of on arithmetic Sequence, then…

A: First term , a1 = x+2 Second term, a2 = 3x -8  Third term, a3 = 4x +2  Eighteenth term, a18 = ?

Q: Find a, and r for a geometric sequence {a, from the given information. a, =24 and as=648

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

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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: Determine the sum of the geometric sequence if it exist. If the sum does not exist, write DNE. 6, 2,…

A: Explanation of the answer is as follows

Q: Write an explicit formula for am, the nth term of the sequence 35, 38, 41, ...

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Q: B. Write a formula for the general term of each infinite sequence. 1. 3, 5, 7, 9, ... 2. 1, 4, 9,…

A: As per the company guidelines we are suppose to answer first question of two subparts.Kindly repost…

Q: find the sum, if it exists, of the infinite geometric sequence described by an =64(1/4)n-1

A: Sum = a/(1-r) ; where 'a' is first term and 'r' is the common ratio.

Q: both questions

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Q: Determine the sum of the geometric sequence if it exist. If the sum does not exist, write DNE. 2, ½,…

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Q: For Exercise, find the indicated term of a geometric sequence from the given information. 16 and r =…

A: We will use the term formula of geometric series And use n=5 in it

Q: B. Write the last four terms before a, of the geometric sequence in which a, and r are as follows:…

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Q: If 4x,x+2 and x-5 form in arithmetic sequence,what is the value of x?

A: Given         4x  , x+2 and x-5 from in arithmetic sequence.      Since   4x  , x+2 and x-5 are in…

Q: For the given geometric sequence. Find the sum of the first 6 terms of -2,2,-2,2,….

A: Sum of geometric progression

Q: Find the specified term of the arithmetic sequence that has the two given terms.a11; a1 = 2 + √2,…

A: a1=2+2a2=3

Q: Find the sum Sn of the arithmetic sequence that satisfies the stated conditions.a1 = 40, d = -3, n =…

A: Formula to find the sum of arithmetic series helps to find the required sum. Formula to find the…

Q: The first term a, of a geometric sequence is 10 and the common ratio r is 5, find the sum of first…

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Q: Find the 22" term of the arithmetic sequence whose common difference is d=2 and whose first term is…

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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: If the 100th term of an arithmetic sequence is 589, and its common difference is 6, then its first…

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

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Q: For Exercise, find the number of terms of the finite arithmetic sequence  11, 10.7, 10.4, 10.1, … ,…

A: Given, terms of the finite arithmetic sequence11, 10.7, 10.4, 10.1, …  −3.4