Let S denote the sum of the terms of an infinite G.P. and o denote the sum of the terms.show that the sum of the first n terms of this geometric progression given by s1-S-o)'] is given by S1-

Q: 1. Find the sum of the following infinite sequence: 40, 20, 10, …

A: A detailed solution is given below.

Q: bn Уп? + 6п — п,

A: Given that the sequence bn=n2+6n-n where n∈ℕ and ℕ is the set of natural numbers. We have to…

Q: Find the first five terms of the explicit arithmetic sequence. an = 4n 2 %3D O 2, 3, 4, 5, 6 O 6,…

A: we have to find the first five terms of the explicit arithmetic sequence an=4n-2 .

Q: 1. Find the first four terms of the sequence whose nth term is an = 2 + 3n. * 5, 7, 9, 11 O -1, -4,…

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Q: Find the first five terms of the given recursively defined sequence. a,= 2(a,1 – 2) and a, = 3 %3D n…

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Q: In week 1, 4 persons were infected by a virus, 16 persons in week 2, 36 in week 3, and 64 in week 4.…

A: Given that, In week 1, 4 persons were infected by a virus so consider a1=4 In week 2, 16 persons…

Q: Find the first five terms and the 14" term of a sequence with 2n +1 general term a, 2n-1

A: Given,         The first five terms and the 14th term of a sequence with the general          term ,…

Q: 5. Find the first five terms of the recursively defined infinite sequence: а, %3D 2, а, %3D5 & a,…

A: a1=2, a2=5 and ak+1=9ak-4ak-1

Q: The sum of the first 20 terms of the sequence O.7,0.77, 0.777,.. is

A: We have to find the sum of first 20 terms of the sequence: 0.7, 0.77, 0.777, ..... Assuming the…

Q: If P1 requests an additional instance of each of A and C, that is, P1's request becomes (2, 4, 6),…

A: Given that, P1 and P3 will be starving for resource C and the system will be in a deadlock.…

Q: Write out the first 10 terms of each of the following sequences (starting with ao). Then give either…

A: (a) an = 3n + 4For n = 0,

Q: (b) Generalize: if the numbers 1 to n are placed around a circle in some order, what is the best…

A: (b) If the numbers 1 to n are placed around the circle in some order, the best possible lower bound…

Q: If an+1 4a, is the difference equation for a sequence which begins with ao = 2 then what are each of…

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Q: 2. The missing term of the geometric sequence 45, [ ],1620, . is ...

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Q: Find all arithmetic progressions with a difference 10 formed of more than 2 primes.

A: We have to find all arithmetic progressions with a difference 10 formed of more than 2 prime.

Q: Find the infinite sum of the geometric sequence with 2 if it exists. 7 a = 4, r = -

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Q: 9 16 2' 3' 25 What is the 30th term of the sequence 4, -- -

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Q: The sum of the first n terms of a sequence is (17n^2 )– 11n. Determine the 20th term.

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Q: QUESTION 8 Identify the 25th term in the progression 7, 10, 13, … 25th    1. 25   2. 79     3.…

A: Term in the progression 7, 10, 13, …25 To find 25 th term

Q: Start with any arithmetic sequence of the form s(n) = an + d for n=1,2, ... and fixed positive…

A: Consider an arithmetic sequence of the form Sn=an+d for n=1,2,3... and fixed positive integers a and…

Q: Find the first 5 terms of the sequence defined byan = 10/n .

A: Consider a sequence an. The first n terms of the sequence are given by: a1, a2, a3,...an

Q: 3. Find two possible next terms of a sequence 2, 8, 9,17 that is neither geometric nor www…

A: Given the sequence 2,8,9and 17. We need to find the 2 possible next terms of a sequence.

Q: Write down the first five terms of the following recursively defined sequence. a₁ = -2; an+1 = -2an…

A: In the given problem it has been given that  a1=-2 an+1=-2an+7 the aim is to find the first five…

Q: Find a closed formula for the sequence defined recursively by bo = 2, bị 3 and b 3b-1 - 2b-2 for…

A: Given sequence is given by  bn = 3bn-1 - 2bn-2 and b0 = 2, b1 = 3. So, b2 = 3*3 - 2*2 = 5 b4 = 3*5 -…

Q: Write down the first five terms of the following recursively defined sequence. a1 = -5; an+1= -2a, +…

A: Given sequence is  an+1=-2an+5with a1=-5To find the first five terms:

Q: Suppose that the sequence {ax} is =0 2, 4, 6, 8, 10, 12, 14, 16, .. What is a1?

A: The given sequence {ak}k=0∞ is -  {ak}k=0∞ = 2,4,6,8,10,12,14,16,18,......... The first tern of the…

Q: Suppose that the sequence {ax}ı is k= 1,3, 5, 7, 9, 11, 13,.. What is a;?

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Q: 2n – the first six terms of the sequence defined by an = Зп + 1 az = Az =

A: Solution of the problem as follows

Q: 10. (a) Explain why the first n natural numbers, {1. 2, 3, -, (n-1), n}, is an arithmetic…

A: 10. In this question, we need to show that the sum of first n natural numbers is 12nn+1 and then we…

Q: A sequence is said to be an increasing sequence if n+1 n+1 Sn2Sn+1 c O n+1

A: I will use the definition of increasing sequence.

Q: Determine the sum of the first 6 terms of the geometric sequence. 1,2, 4, .. So

A: A geometric progression is a type of sequenc in which ratio of two consecutive terms is always a…

Q: 2" An 2n+1

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Q: Prove { (8n-7)/n} n=1 to infinity is an increasing sequence.

A: If we take the sequence as {Un}, and if we can able to show that for all n=1,2,3, ...  Un+1>Un…

Q: Write down the first five terms of the sequence ɑn = 9n n+15 a2 = az = a4 = as =

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Q: If the sequence ~ 9- an - 3 :} converges to 6, then the sequence {an} converges to 9.

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Q: the n^th term of the following sequence 1,4,7,10,...is

A: For given sequence a1 = 1 a2= 4 a2 = a1 + 3

Q: If the first term a, and common difference d of an arithmetic sequence are 3 and respectively then…

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Q: Find the infinite sum of the geometric sequence with 3 if it exists. a = 2, r =

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Q: Write down the first five terms of the following recursively defined sequence. aj = 2; an+1 = -2a +…

A: To write down the terms of recurssive relation,   1) Put value of a1 in recurssive relation we get…

Q: Find a closed formula for the sequence defined recursively by bo = 2, by = 3 and b, = 3b,-1 – 2b,-2…

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Q: 1.) Show that the sequence 2,11, 20, 29, ... is arithmetic.

A: we have to show that the given sequence is arithmetic

Q: 35. Prove that the sequence {n!}^, beats the sequence {2"}-1-

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Q: The limit of the sequence an= (1+)* -- is: 3n (a) – e (b) el7) (c) e-3 (e) None a b C d e

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Q: a. What would be the population size in 7 years. b. Fund the sum of the first eight terms of the…

A: Given; P0=5000 Rate=2%=0.02 the sum of the first eight terms of the sequence 18,-14,12,.... Formula…

Q: What is the fourth partial sun for the geometric sequence a1=18 and r=2

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Q: The sum of first 6 terms of an arithemetic progression is 42 the ratio of its 10th term to its 30th…

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Q: State the first four terms of the geometric sequence with a =5 and r = 0.6 and give the limiting sum…

A: For the given geometric sequence, a = 5 and r = 0.6 We have to find the first four terms of this…

Q: 1. 3,6, 12,... n = 12 27 2. 12, 9, 4 n = 5 ....

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Q: Determine whether the sequence {5n−7 / 3n+4} is increasing, decreasing, or neither.

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