Q1/ A geometric sequence whose terms are positive and the sum of the first and second terms is 36, and alone the third is equal to = 3 Find the fifth term? Q2/If the fifth term in an arithmetic sequence is equal to 9 and the eighth term is equal to 15, find the sequence.

Q: If third and seven terms of geometric sequence is 45 and 100 respectively.then find its nineteenth…

A: Given data: The third term is a3=45. The seventh term is a7=100.

Q: If the 3rd term of a geometric sequence is 28 and the 7th term is 448. Find the common difference…

A: The given data is: The 3rd term of a geometric sequence is 28 and the 7th term is 448. To find the…

Q: An arithmetic sequence has a its 5 th term equal to 22 and its 15 th term equal to 62. Find its 100…

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Q: Find the 5th term of the geometric sequence with first terma1 = 5 and common ratio r = - 2

A: A geometric sequence is a sequence where each term is found by multiplying the previous term by a…

Q: Find the 65th term of the arithmetic sequence with first term 3 and common difference -1/2 (negative…

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Q: A geometric sequence whose first term = 2 and whose sixth term = 64, i) find the first six terms ii)…

A: The nth term of a geometric progression or a geometric sequence with first term and common ratio r…

Q: Determine the first six terms of the sequence defined by t₁ = -5 and t = -3t-1 + 8. -5, 23, -61,…

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Q: Find the sum of the first 12 terms of the geometric sequence 3, -9, 27, -81, 243, ..

A: Geometric sequence 3,-9, 27,-81, 243.... To find :- Sum of first 12 terms of given sequence

Q: 11 and the 13" term, a,3, is equal to 33. Find the value of the 17t" For a given geometric sequence,…

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Q: Find the sum of the first 94 terms of the arithmetic sequence   11,15,19,23,27, . . . .

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Q: 2. The third term of an arithmetic sequence is x and a, = 19x + 6. Find the twelfth term. 3. Php…

A: given

Q: 3. In an arithmetic sequence if 5th term value is 26 and 10th term value is 51. Find 15th term…

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Q: Find the sum of the first 70 terms of the arithmetic sequence with the first term 6 and common…

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Q: Find the 38th term of a sequence where the 15th term is 0 and the common difference is 1.

A: see below the answer  here we have use the sequence  as arithmetic sequence

Q: 4. The total amount of water poured to a container is 1350 liters. During the first day the amount…

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Q: The first term in an arithmetic sequence is 11 and the sum of the first 15 terms is 900. What is the…

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Q: The geometric mean between the first two terms in a geometric sequence is 32. If the third term is…

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Q: Find the 13th term of the geometric sequence 7, -35, 175,

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Q: The third term of a sequence is 64 while the seventh term is 4. Determine the sum of the first ten…

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Q: Find the 10th term of the geometric sequence. aj1 = -5, r = - %3D %3D 10th term:

A: →nth term any geometric sequence is given by,                            an = a1 rn-1 , Where a1  is…

Q: What are the explicit equation and domain for an arithmetic sequence with a first term of 7 and a…

A: The Arithmetic Sequence Explicit formula allows the direct computation of any term for an arithmetic…

Q: Find the sum of the first 13 terms of the arithmetic sequence. 5,9, 13, 17. . What is the sum of the…

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Q: Find the tenth term of the sequence. 1,0, -3, -8, - 15, ... The tenth term is

A: Given series: 1, 0, -3, -8, -15

Q: A geometric sequence is a sequence in which theof successive terms is constant.

A: In a geometric sequence, the ratio between successive terms is constant. Geometric sequences grow or…

Q: The first, third and sixth terms of an arithmetic sequence form 3 successive terms of a geometric…

A: We use basic of arithmetic progression and geometric progression.

Q: What is the first term of a geometric sequence which fourth term is -40 and with common ratio of -2?

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Q: Find the first four terms of the arithmetic sequence whose first term is 9 and whose common…

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Q: A sequence in which each term after the first differs from the preceding term by a constant amount…

A: A sequence in which each term after the first differs from the preceding term by a constant amount…

Q: Determine the sum of the first 8 terms of the geometric sequence. 3,-3, 3,

A: Given a geometric sequence.

Q: Find the sum of the first 40 terms of the arithmetic sequence with first term 3 and 40th term 120

A: According to question given thatwe have to calculate the first 40 terms sum of the arithmetic…

Q: sequence

A: We have to determine the common ratio of the given sequence

Q: 4. The 1st term of an arithmetic sequence is -168 and every term after the first is 8 more than term…

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Q: 5 th term of a geometric sequence is -80 and its 10 th term is 2560. Calculate the following. Show…

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Q: Find the first term and the common difference of the arithmetic sequence whose 7th term is −5 and…

A: In airthmetic sequenceuse formula nth term tn=a+n-1d7th term t7=a+7-1d=-5a+6d=-5--116th term…

Q: Find the sum of the first 30 terms of the arithmetic sequence: 7, 3, -1, -5, . .

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Q: Find the sum of the first n terms of the geometric sequence with the given values. a, = 320, r= k --…

A: Given: a1=320r=-k2n=10 Also, the sum of  first n terms of the geometric sequence for negative value,…

Q: The 9th term of an arithmetic sequence is 19 and the 20th term is 20.3 What are the first three…

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Q: The SECOND and THIRD term in a geometric sequence is 16 and 5th term is 54. Find the sum of the…

A: Topic:- sequence and series

Q: The first three terms of a geometric sequence are as 64, 32, 16 Find the next two terms of this…

A: Geometric Series: The general geometric series is in the form of a,ar,ar2,ar3,… where a is the first…

Q: Find the formula of the Sequence. 1.) 2,1,3,4/3,15/4..., or 2, 2/2, 3/1, 4/3, 5(3)/4,...-

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Q: How many terms of the arithmetic sequence -2,3,8… must be added to get 1573? Thank you for the help

A: Sol:- As we Know that . nth term in arithmetic sequence is given by :- an=a1+n-1dWhere d= common…

Q: The sum of the first 10 terms of an arithmetic sequence is 530. What is the first term if the last…

A: I have appended the formula used in the solution part.

Q: the sum of the first 40 terms of the arithmetic sequence.   −16​,−25​,−34​,−43​,...

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Q: (2п)! An

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Q: 2) The sum of the first 16 terms of an arithmetic sequence is 212 and the fifth term is 8. a) Find…

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Q: Find the first term and the common difference of the arithmetic sequence whose 9th term is – 17 and…

A: The general form of arithmetic sequence is a,a+d,a+2d,......,Where a  is the first term of the…

Q: The product of the first term and the 6th term of an arithmetic sequence is -38. The sum of the 3rd…

A: Topic - arithmetic progression

Q: term in a geometric sequence whose 3rd term is 5/4 and 6th term is 10?

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Q: Find the first term and the common difference of the arithmetic sequence whose 11th term is – 15 and…

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Q: Find the nth term of a sequence whose first several terms are given. 2/3, 3/4 , 4/5, 5/6

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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.