How many terms are there in each of the following​ sequences?   a. 36 ​,37 ​,38​, 39 ,​..., 336  b.​ 1, 2 ​, 22 23​,​..., 250  c. 100 ,  200​, 300​, 400​,​..., 40000  d. 1​, 2, 4​, 8​,16, ​32​,​..., 4096

Q: Find the explicit formula for the given sequence. 2, 8, 32, 128, ....​

A: SOLUTION-

Q: 5. The sum of the first n terms of a sequence is called the nth sum and is denoted by S.

A: An arithmetic sequence is a series of numbers that have the same common difference and the sum of…

Q: Give the common ratio of the * sequence 10, 2, 2/5 , .... O 1/ 5 O 5 O -5 O - 1/ 5

A: common ratio is the ratio of particular term to previous term.

Q: How many terms are there in each of the following sequences? a. 53, 54, 55, 56, ..., 253 b. 1, 2,…

A: Note: There are many subparts in the questions. So I will answer the first three subparts from the…

Q: Suppose a, is the sequence such that a, = -3 - (-1)". Find 25 Li-5 đị. O a. 325 - 35 O b. -3 Ос. 3 O…

A: Given sequence is an=−3⋅−1n. We have to find the ∑i=525ai.…

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: The first four terms of the sequence defined by An — пар-1 + п*a,-2, do — 3, а1 = 3, a1 = 4 are ao =…

A:

Q: Given the sequence defined by b n= (−1) n-1n, which terms are positive and which are negative?

A:

Q: How many terms are there in each of the following sequences? a. 33,34,35,36,....,233 b.…

A:

Q: Find a, and r for a geometric sequence (a,) from the given information. 47 az = 47 and a, 8 a, = r =

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: For the sequence defined by: a1 = 4 - 2 an an+1 Find: a2 : = az a4

A:

Q: Let (a,) be the sequence defined by a¡ = 5 and a, = 2a,-1 – 3 when n > 2. What is a4?

A: Here an be the given sequence which is defined by a1=5 and an=2an-1-3 when n≥2 . We have to find a4…

Q: How many terms ae there in each of the following sequences? A.   1, 3, 9, 27, 81, 243, ..., 6561…

A:

Q: How many terms are there in each of the following sequences? a. 56,57,58,59,...,456…

A:

Q: Which explicit formula describes the sequence {1,2/7,4/29,8/343,...}?

A: gdfge

Q: a1 = -1, and for n = 2, 3, 4, .. What is the common ratio, r, for this sequence? O -- O r--1

A:

Q: Which of the following represents the Fibonacci sequence? O a1 = 1, a2 = 1, an = an-1 – an-2, for…

A: We will find the Fibonacci sequence.

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: Find the explicit formula for the given sequence. 2, 8, 32, 128, ....

A: TO find the explicit formula of given sequence .first check the common ratio terms since ratio is…

Q: Find the explicit formula for the given sequence. 2, 8, 32, 128, . .... a = 2.4"-1 A a = 8.4"-1 %3D…

A: We have the given sequence is 2,8,32,128............

Q: The third term in the sequence with a1 = 2 and an = an-1+4n where n > 1 is, O 22 O 10 O 14 O 26 O 2

A:

Q: 4. What are the first five terms in the recursive sequence defined by the following? a1 = %3D an =…

A: If you have given a recurrence sequence and given first term then using first term in the recurrence…

Q: 5. What are the first five terms in the recursive sequence defined by the following? aj = 0 Chn =…

A: Given: The recursive  equation as  a1=0,an=an-1-1.4 To find: First five terms of the given recursive…

Q: The first four terms of the sequence defined by an = nan 1+En'a, 2, ag = 2, a, = 6 are O ao = 2, a1…

A: Note:- For given problem Either options are wrong because according to problem a2=6 but in option…

Q: Find the So. for each of the following sequences. 16 32 i) 20, 8, ****** 5' 25' 3-3 " 4 16 ii) 12,…

A:

Q: Find the explicit formula for the given sequence. 2,8, 32, 128, ...

A:

Q: Given that {a,n} is a sequence such that n 2" P. = II a = +1 %3D ak = n2 + 1 k=1 Find n (k? + 1)ak…

A:

Q: Given that a is a geometric sequence and az = and a5 what is a12?

A: Let the first term is = a and common ratio=r Given that

Q: 1. What is the 16th term of each sequence shown below. a) 2, 10, 18, ...

A: a. 2,10,18,.... To find the 16th term.

Q: For the sequence defined by: ai = 2 1 + 5 An аn + 1 — Find: a2 az = a4 = II

A: To find  a2 , a3 , a4  substitute n=1,2,3 respectively  in the given equation.

Q: 1 The following sequence is geometric: a, = 8, and a,=--a, , for n = 2, 3, 4, ... %3D O True O False

A: The given sequence a1=8 and an=-16an-1 for n=2,3,4,......

Q: The general term of the sequence 1, 24'8 ... , starting by n=1 is to0 1 (i) n=1 +00 1 (ii) n=1…

A:

Q: | 1. What are the first five terms in the recursive sequence defined by the following? = Ip An =…

A:

Q: How many terms are there in each of the following​ sequences?   a. 36​ ,37​, 38​, 39​,​..., 136 b.​…

A:

Q: Given the following three sequences: I. 2, 4, 6, 8, 10... II. 2, 4, 8, 16, 32... III. а, а + 2, а +…

A: Given sequence are                I .   2, 4, 6, 8, 10, _ _ _               II .   2, 4, 8, 16, 32 _…

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

A:

Q: In an arithmetic sequence a1, a2, · ·-, an , if the first term is 7 and the common difference is 5,…

A: We use arithmetic progression formula an = a + (n-1)d

Q: 13.What is the 3rd term of the sequence defined by an = (-2n)", %3D O A. 216 о в. 276 O C.-216 O D.…

A:

Q: Find the first three terms of the a, = 4 sequence: an+1= 5n + 1 an 6. O 4, 4, 22/3... O 4, 22/3,…

A:

Q: or each of the following sequences (eithe 9, 18, 27, 36, 45, .

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: For the trihonacci type sequence begging 1,2,2 write the next five terms

A: To write the next five terms of the tribonacci sequence

Q: 1. Find an explicit formula for the general term of the given sequence: 5, 10, 20, 40, 80,…..

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: In geometric sequence a1, a2, · -, an , if az = 416 and a5 6656, then the common ratio is O 64 O 4 O…

A:

Q: 1. a) Determine the first three terms of each sequence, where ne N. b) Determine whether each…

A:

Q: 1. What are the first five terms in the recursive sequence defined by the following? a1 = 150 an =…

A:

Q: The first four terms of the sequence defined by an = nan 1+n'a, 2, ao = 2, a1 = 6 are %3D O ao = 2,…

A:

Q: I) Consider the sequence 4, 6, 8, 10, 12, (a) If {an} denotesthis sequence, then n=1 a1 =

A: Given the given sequence is 4, 6, 8, 10, 12, ···

Q: What are the terms ao, aj, a2, and az of the sequence {an}, where an equals b) (n + 1)"+l? d) [n/2]…

A: a. an=2n+1. The terms become a0=20+1=1; a1=21+1=3; a2=22+1=5; a3=23+1=9 Therefore, the terms of the…

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

A:

Q: Find a1 and r for a geometric sequence {a, from the given information. 41 az = 123 and a,= 9 a1 r=

A: The given terms of the geometric sequence,a3=123 and a6=-419

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.