In an arithmetic progression of n terms (n is even), the two middle terms are p-q.p+q respectively. Prove that the sum of the squares of all the term of the progression is n p + 3

Q: Let an​ be an arithmetic progression, for which a3​=13 and a11​=25. Find a7​

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Q: An auditorium has 80 seats in the first row and the number of seats increases according to an…

A: If a1 is first term of arithmetic progression and d is common difference then nth term of arithmetic…

Q: 4. Find the 52nd term of the arithmetic sequence: 3, 7, 11, 15, ...

A: To find The 52nd term in arithmetic sequence 3,7,11,15,....

Q: Write the first four terms of the sequence defined by the recursive 2+an-1 formula a1 = -14 . /(5…

A: The solution are next step

Q: Write a recursive formula for finding the nth term of each arithmetic sequence. 15.75, 14.25, 12.75,…

A: First Term of the sequence is a1=15.75 common difference is: d=an-an-1=a2-a1=14.25-15.75=-1.5…

Q: A town has a population of 5000 persons,  but is expected to grow by 2% every   What would be the…

A: As per bartleby guidelines for more than one question asked only first is to be answered please…

Q: Find the common difference and the sum of the first 5 terms of the arithmetic sequence. an = 5n – 2

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Q: Find the sum of the finite geometric sequence. E(-3)" - (-3)" – 1 n-1

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Q: A town has a population of 5000 persons, but is expected to grow by 2% every year.    (i) What…

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Q: What is the formula for the arithmetic sequence if the sum of the same sequence is given by sn = 2n…

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

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Q: Find the 12th term of the geometric sequence 5, 20, 80, ...

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Q: find the values of k so that the numbers 2k+1, 3k+4 and 7k+ 6 form a geometric sequence

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Q: Write a recursive formula for an, the n" term of the sequence 17, 21,

A: Given that: The series is : 17, 21, 25, ....

Q: 3. Find x so that x + 6, x + 12 and x + 15 are consecutive terms of a Geometric Progression.

A: We want to find value of x

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

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Q: Find the first five terms of the sequence 2" -1 n 1, 2, 3, .. аn n2 1

A: Given: -

Q: the sequence {12, 4, −4, −12, −20, } assuming that the pattern

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Q: Find x so that x, (x + 2), and (x + 3) are consecutive terms of a geometric sequence.

A: In this question, we will find the value of x which will satisfy the conditions of a geometric…

Q: Find the sum of the first 30 terms of the arithmetic sequence. an = -3n + 27

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Q: Let an​ be an arithmetic progression, for which a1​=15 and d=3. Find the sum of the first 10…

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Q: 4 Chose the formula for the nth term of the Geometric Sequence: 6, 4, 4, 10

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Q: Consider the sequence 8, 5, 2,-1.........-52 a) is the sequence an arithmetic progression? Why or…

A: Arithmetic Progression: A sequence is said to be an arithmetic progression, if the difference…

Q: Find all triples of squares of natural numbers in arithmetic progression such that b2-a2=c2-b2.

A: Find all triples of squares of natural numbers in arithmetic progression such that b2-a2=c2-b2

Q: (a) A town has a population of 5000 persons, but is expected to grow by 2% every year. (i) What…

A: i) Given: A town has a population of 5000 persons, but is expected to grow by 2% every year. Find…

Q: b) In an Arithmetic Progression the 8th term plus the 4th term equals the 13thterm. If the 18th term…

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Q: In an Arithmetic Sequencea1, a2,.an, the first term is 7 and the 11 term is 57, then S is

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

Q: Find the common difference and the sum of the first 8 terms of the arithmetic sequence. an = 4(n-1)…

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Q: Find a n for the geometric sequence a 1 =-4; r = - 2, n = 10

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Q: Find the 8th term in the sequence 18n-36.

A: Put n= 8

Q: Find t for the arithmetic progression 19, 14, 9, .. t

A: Given : Arithmetic progression : 19,14,9,...

Q: An arithmetic sequence is a sequence in which the___between successive terms is constant.

A: An arithmetic sequence is a sequence in which  the difference between successive terms is…

Q: Find the sum of the first 50 terms of the arithmetic sequence. an -5n – 6 ||

A: The arithmetic sequence is given by an = -5n-6 To evaluate: The sum of the first 50 terms of the…

Q: An arithmetic sequence has the 5th term equal to -64 and the 14th term equal to -1. Calculate the…

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Q: Let an​ be an arithmetic progression, for which the first term a1​=1 and common difference d=1. Find…

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Q: Find the 15 term of the arithmetic sequence 1.18, 1.26, 1.34, ... the 15h term is

A: topic - arithmetic sequence

Q: A town has a population of 5000 persons, but is expected to grow by 2% every year. (i) What would…

A: Solution: From the given information, the town has a population of 5000 persons. But it is expected…

Q: The general term of a sequence is given an = -2(n - 1)! and involves a factorial. Write the first…

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Q: Find a formula for the general term a, of the sequence, assuming that the pattern of the first few…

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Q: Find a closed formula for the sequence with recursive definition An = 2an-1 – an-2 with a1 = 1 and…

A: The closed formula for a sequence is used to define the general term of a sequence. The recursive…

Q: Find the indicated term of the geometric sequence. 6th term of 3, 3/4, 3/16…

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Q: Find the firstive terms of the recursive sequence 2 a, -3 a,-2a+1

A: The terms of recursive sequence can be obtained by substituting the value of n, the the value of…

Q: Find the first six terms of the recursive sequence.  a1=1, a2=2, an+2=an+1+2an

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Q: Write a recursive formula for the sequence 8, 10, 12, 14, 16, .. Then find the next term.

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Q: In the arithmetic progression 2,5,8,... upto 50 terms, and 3,5,7,9,.. upto 60 terms, find how many…

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Q: Find the 6th term of a geometric sequence with a 1 = −3 and r= 2.

A: Find the 6th term of a geometric sequence with:

Q: Give the first five terms of the sequence: a, = n° -2n %3D

A: Given,           The sequence is an=n3-2n.

Q: Find the generating function of the sequence Un = n2

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Q: Find the first four terms and the eighth term of the sequence.

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Q: 9. Find the value of x and y if x-y, 7x+y-1, and -5y are consecutive terms of an arithmetic…

A: As per the instruction, we will be answering only the first question. We need to find all the value…

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.