(1+√5) −(1- 2√5 - and the The nth term of the sequence in number 1 is given by an ratio, between two consecutive terms of this sequence converges to a special number which is referred to as the golden ratio. Which of the following is the exact value of the golden ratio? 1-√√5 2 1 0 1+√5 2

Q: Use the difference an+1 – an to show that the sequence {n – 9"} is strictly increasing or strictly…

A: here sequence is n-9n so  an+1 = (n+1) - 9n+1          = n+1-9(9n) an = n - 9n so now an+1 - an =…

Q: Please solve (a)

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Q: Find the 11th term of the harmonic sequence1/5,1/8/1/11,1/14,. . .

A: harmonic progression is 1arithmetic progression the given series has a pattern of = 13+previous term…

Q: Qw.146. explan the formula, the imags (a,b)and find the next sequence with its image

A: Ans- These are some of the identities related to the Fibonacci sequence, which is a sequence of…

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Q: The number sequence a1, a2, a3, .... is defined by a1 = 8 a2 = 24 and recursion formula 4an + 1…

A: We need to show that an=5n-12n-2 for a1=8 and a2=24  The given recursion formula is…

Q: find a formula for the nth term of the sequence. √5 - √4, √6 - √5, √7 - √6, √8 - √7, . . .

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Q: 4n2-11 Q2. Determine if the sequence converges, and if so find its limi 12n2+4n-8.

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Q: (a) Suppose that (în) is a sequence of real numbers. Define what it means to say that the sequence…

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Q: f(n)=(n-1/2) (n-1/3) Its n-1 over 2 and n-2 over 3 Write the first six terms of the sequence…

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Q: ommon e 2 and the last (2m + 1) erm /2. If the middle term of both A. P. and G. P.

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Q: xk+1+2xk for k20. Find a general formula for xk. Be Suppose that the sequence x0, x₁, x₂... is…

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Q: Which of the following is the generating function for the sequence 5, 5, 5, 5,. ? O A. G(x)=(1-x)-1…

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Q: What is the formula for the nth term tn of the sequence: t2 = 3, tn = (-3/2)tn-1 , n is greater…

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Q: Write the first five terms of the sequence with the given nth term. = sinl an a a3 as

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Q: 8n-4 Determine if the sequence An converges or diverges. If the sequence 67 –4 converges, to what…

A: Given : an=8n-46n-4   To check : an converges or diverges

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: vīz, vi2+ V12 , V12+ V12+ V12 ,. .... Consider this sequence: i.e., a, = V12, a,1 = V12+a, ,n>1 Use…

A: Given a1=12 and an+1=12+an, n>1 First of all, we will write the first 10 terms in the given…

Q: Let bo, b,, b2, ... be the sequence defined by the explicit formula b, = c. 6" + D(-5)^ for each…

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Q: Solve the recurrence defined by a for n ≥ 1. an 3(6^n)-2 3 and : 6an-1 + 5 an =

A: As per the guidelines I am answering only one question at a time. an=6an-1+5, a0=3