, n=1,2,3. is a sequence of real numbers defined by a, = /2 %3D %3D and for n21, a = 2,/2+a, .

Q: A sequence is said to be decreasing sequence if Vn > 1 'n+1°n =S .a .b O n+1 2n.cO n+1 n+1d0 n

A: Option (d) is correct.

Q: For the sequence 1, 4, 7, 10, .. . its nth term is

A:

Q: The limit of the sequence a, = (-1)"2 is equal to %3D Select one: True O False

A:

Q: a. 2, 8, 26, 80, 242 b. 1, 2, 3, 4, 5 c. 1, 3, 9, 27, 81 d. -1, 2, 8, 26, 80

A: First five terms of the sequence defined over the natural numberswith the explicit function…

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: Suppose that a sequence is defined as follows. a=2, a,=-3a,-1 for n22 List the first four terms of…

A: Given :              a1 = 2              an = -3 an-1 + 5 To find :                    The first…

Q: Find the first six terms of the piecewise sequence: S(- 2)" – 4 if n is even An 3n -1 3 if nis odd

A: solutiongiven an=-2n-4 , if n is even3n-1-3 , if n is oddfirst six terms of the pieccurce…

Q: I. Find the first three terms of the sequence whose nth term is given by the formula. Show the…

A: We need to determine the first three terms of the given sequence using the given general formula.…

Q: Find a formula for the nth term of the sequence: 1,1//8,1//27,1//64, ... Select one: O a. a, =1/n…

A:

Q: For the sequence defined by: a1 = 2 1 + 2 an an +1 Find: %3D a4 -

A:

Q: 4. The same strategy from the previous page can be used to find specific entries. Given the function…

A: Generalize the terms in the sequence and find the elements  asked.

Q: > The general term of the sequence 1,!! ! , starting by n-0 is (6) 2n+1 (ii) (iii)None of these

A:

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

A:

Q: (b) Give a recursive definition of the sequence {dx},k =1, 2, . .. if (a) dk = 4k – 2; (b) dɛ =…

A: According to the guidelines, I am solving a,b and c part only.But part d can also be solve using…

Q: Let an be the n th element of the sequence 5,8,11,14,17,.., then an=d xn+c for constant values d and…

A:

Q: Find the sum of the sequence. I (k° +4) k=1

A: Given sequence is

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: Match the sequence with the given nth term with its graph. 10n an n + 1 an an 10 10 8. 8. 4. 2 4 6 8…

A: here given  an = 10n/(n+1) for plotting put point 1,2,3,4...... first wwe put 1 a1= 10(1)/(1+1) = 5…

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: Compute the first 6 terms of the sequence {an} where An-1+n a1 = 1 and an for n > 2.

A: The given sequence,a1=1 and an=an-1+n2 for n≥2

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

A:

Q: You may assume that 1, 1, 2, 3, 5, 8, ... has generating function 1-x – 2² (because it does). Use…

A: In the problem, it has been given that 1,1,2,3,5,.... has a generating function 1(1-x-x2) When we…

Q: Find first 5 terms of the following sequence: {an} given by a, = (-1)" („ 3n-2 n2-2n+3 99 Evaluate:…

A: First five terms of the sequence an=(-1)n(3n-2n2-2n+3) at n =1  a1=-3-21-2+3=-12 at n =2…

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

A:

Q: This is sequence and the is equal to

A:

Q: Find first five terms of the sequence. An Зп + 1 bn = (-1)"n² 2n Сп n ||

A:

Q: Match the sequence with the given nth term with its graph. 10n n + 1 an an 10 8 1+ .. 6. 2 4 6 8 10…

A:

Q: What is the sequence function (an) for the following 1 2, 1.2, 3 3

A:

Q: Find an expression for the n th term (t) in each of the following sequence: 1 1 1 1 1 >... 3 4 5 6.…

A:

Q: 9. Find the explicit formula for a sequence satisfying а, %3D10а,, + 25а, _,n22 n-1 а, %3D 3, а,…

A:

Q: A sequence is said to be decreasing sequence if Vn 2 1 =DS n+1 aO .b O n+1 n+12s.cO 2n.d O n+1

A: Option (b) is correct.

Q: For the sequence defined by: a1 = 2 2 An+1 = an - 5 Find: az = az = a4 =

A: Given : a1 = 2an+1 = 2an - 5

Q: Suppose that a sequence is defined as follows. a1=-5, a,=4a, +10 for n>2 List the first four terms…

A:

Q: Use the given nth term formula to compute the first tên terms of the sequence. n(2n+1) 6. аn 3 2

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: If t_n=3.5n+4.5, find t_1 ,t_10 and t_n+1-t_n. Is 85 a term of this sequence

A:

Q: Find the first four terms and the seventh ferm (n = 1,2,3, 4 &7) if the general ferm (-1)" of the…

A: Here, the sequence is

Q: Find the explicit formula of the following sequence. {8, 4, 2, 1, ...} f(n) = a, · 3n-1 a

A:

Q: Find an explicit formula for a sequence of the form  a1,  a2,  a3,     with the initial terms given…

A:

Q: For the sequence defined by s, = E(? – i), complete the first three rows of the difference table i=1…

A:

Q: Suppose that a sequence is defined as follows. a1=-5, a,-4a, +10 for n>2 List the first four terms…

A:

Q: Let an be the nh element of the sequence 5,8,11.14,17,., then an.dxn+c for constant values d and c.…

A: What is d??

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

A:

Q: If the explicit nth term formula for the given sequence is an = 2n2 + bn +c, then b= and c= 5, 10,…

A: Plugging n=1, an=2n2+bn+ca1=212+b1+c5=2+b+cb+c=3 Plugging n=2, an=2n2+bn+ca2=222+b2+c10=8+2b+c2b+c=2

Q: The sequence fn is given as f1 = 1, f2 = 3, fn+2 = fn + fn +1 for n ≥1 How many even terms are…

A: Even numbers : The integer ends with 0,2,4,6 and 8 are even numbers . Euclid division lemma : Given…

Q: For the sequence defined by: a1 = 2 An+1 = +1 - An Find: %3D %3D a4 = %3D 2]

A:

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

A:

Q: Suppose Suppose a,= n2 – 2n + 4. Find a closed formula for the sequence of differences by computing…

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Q: A sequence of the form a, a + d, a + 2d, a + 3d,..., a +nd is called

A:

Q: 16. For what value of n is the following sequence A". If c = 2, find Co. %3D Cn = 2,4,10,23,46,82,…

A:

Q: Find a closed formula for the sequence (Cn)neN defined as follows: if n = 1, Cn = if n = 2, 8. Cn-1.…

A: As per the question we are given a piece-wise defined sequence (cn) and we have to find a closed…

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.