Three numbers, of which the third is equal to 36, form a geometric progression. If 36 is replaced with 20, then the three numbers form an arithmetic progression. Find the initial three numbers.

Q: Given a geometric progression 64, 32, 16,…, find the sum of all the terms from sixth term to the…

A: Solved below

Q: Eighty loaves of bread are to be divided among 4 people so that the amounts they receive form an…

A: Given,          Eighty loaves of bread are to be divided among 4 people so that the amounts they…

Q: The seventh term of an arithmetic progression is 11 and the sixteenth term is 29. Find: the common…

A: Given seventh term of A.P=11 Sixteenth term of A.P=29 We know that nth term of A.P (an)= a+(n-1)d…

Q: b. Find the first five terms of the Geometric progression whose first term is 2 and fourth terms is…

A: As a g.p. is always of the form a,ar,ar2,ar3,... Here a is the first term and r is the common ratio,…

Q: n of a geometric progression is -108 and sixth term The common ratio

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Q: The second term of an infinite geometric progression (|q|<1) is 21 and the sum of the progression…

A: Let the first term= a and common ratio=r  Given the second term= 21 So, ar=21

Q: In an arithmetic progression the first term is 5 and the common difference is 3. The nth term of the…

A: Sum of first n terms = ∑n=1nun=n22a+n-1d           where, a=first term,  d=common difference

Q: Given the first three terms of an arithmetic progression as 2x, x + 4 and 2x – 6 respectively. Find…

A: Hi there, we can answer only one question at a time and you was not specify. so, I have answered…

Q: Find the next three terms of each geometric sequence. 12.-5, -20, -80...

A: Solved below

Q: The 10th term of an arithmetic progression is 4 and the sum of the first 7 terms is -28. Find the…

A: General formula of nth term of arithmetic progression is an=a+n-1d. 10th term is 4, that is a10=4…

Q: The sum of the terms of an infinite geometric progression is 35 and the common ratio is What is the…

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Q: (a) The first 3 terms of an arithmetic progression are ?, 5?, 7? − 4. Find (i) the value of ?,…

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Q: In an arithmetic progression, the sum of the first five terms is 30, and the third term is equalto…

A: We have given  Sum of the first five terns of an arithmetic progression = 30 S5 = 30 Sum of n terms…

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: Given the parameters of an infinite geometric progression, find the sum of its terms. 2 a = 20, r= -…

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Q: If 4, x, y form an arithmetic progression and x, y, 18 form a geometric progression, what is the…

A: Three numbers a,b,c are A.P. then the difference between the two consecutive numbers remains…

Q: If 12 and 384 are the second and seventh term, respectively, of a geometric progression, find the…

A: Since, we have been given that the second and seventh term of a geometric progression are 12 and 384…

Q: The sum of first six terms of an arithmetic progression is 42.The ratio of its 10th term to its 30th…

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Q: In a geometrical progression, the sum of the second and third terms is 9,and the seventh term is…

A: Given Information - In a geometrical progression, the sum of the second and third terms is 9,and the…

Q: In geometric progression if the first term is 2 and 6th term is 6250, then find the common rat

A: We have to find

Q: The sum of three numbers in a geometric progression is 14. If the first two terms are each increased…

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Q: n a geometric progression, the third term exceeds the first term by 9 and the sum of the second term…

A: Topic = Series

Q: Let an​ be an arithmetic progression, for which a2​=5 and a1​=−11. Find the difference of the…

A: The objective is to find  the difference of the progression.

Q: The sum of three numbersin arithmetic progression is 60. If the first be diminished by 3, the second…

A: Given The sum of three numbers in arithmetic progression is 60 and   If the first be diminished by…

Q: The first term and the last term of an arithemetic progression are 17 and 350  respectively . If the…

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Q: In an arithmetic progression the first term is 5 and the common difference is 3. The nth term of the…

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Q: d) What are the extremes of the progression? e) What are the means of the progression?

A: The first and last terms of the sequence are called arithmetic extremes.The terms in between are…

Q: For which term does the geometic Sequence an = -36(?)^:/first have non-integer ralue a

A: Given, an=-3623n-1

Q: The second term of a geometric progression is 2 3 and the fourth term is 1 54 . If all the terms are…

A: We know that a geometric progression is given as: a+ar+ar2+ar3+ar4... where 'a' is the first term…

Q: An arithmetic progression has the first term of 32, the 5th term of 22 and the last term of −28.…

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Q: Three numbers are in an arithmetic progression with a common difference of 6. If 4 is subtracted…

A: Given data is : Common difference is 6 Let the three number in AP is a,a+6,a+12 From question , a-4…

Q: If (4/5) , a,2 are three consecutive terms of an arithemetic progression then find the value of a.

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Q: Find the 20 term of a geometric progression 1,2, 4, ...

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Q: Given the first three terms of an arithmetic progression as 2x, x+4 and 2x-6 respectively. Find the…

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Q: 2. Find the first three terms of geometric Progression whose sum is 342 and product is 74,088 Let…

A: Solution : First three terms of GP are, ar,a,ar Sum of first three terms of GP=342 ar+a+ar=342  …(1)…

Q: Question (3b): In an arithmetic progression the sum of first ten terms is 400 and the sum of the…

A: Given: Sum of first ten terms is 400 and sum of the next ten term is 1000 To find the common…

Q: Find four numbers that form a geometric progression such that the second term is less than the first…

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Q: An arithmetic progression has first term 11 and fourth term 32. The sum of the first nine terms is?

A: Formula,   S(n) = (n/2) * [2a + (n-1)*d]

Q: (b) The nth term of a geometric progression is given by T, Find the sum of first four terms.

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Q: Find the geometric progression if the 5th term is 12 and the 8th term is 324.what is the sum to…

A: Let the geometric progression is a, ar, ar2, ar3, ar4, ar5, .... Given the 5th term is 12 That is…

Q: 3. The sum of three numbers in geometric progression is 52. If 8 is added to the middle number, the…

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

Q: Determine x so that (4x), (5x+4), (3x^2 -1) will be an arithmetic progression. Show complete…

A: We know that in an arithmetic progression the common difference between two consecutive terms is the…

Q: It is given 3, 12, x are three consecutive terms of geometric progression. Find the value of x.

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Q: A geometric progression has 6 terms. The first term is 192 and the common ratio is 1.5. An…

A: Solution and Explanation is given below....

Q: In a Geometric Progression given, find the sum of the first term and the common ratio: an = -96, n…

A: The nth term is given by an=arn-1. The sum of geometric progression is given by Sn=a1-rn1-r.

Q: It is given the first three terms of a geometric progression are 1/5 , 1/25 and 1/125. Find the sum…

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Q: If 7, 9. 8 and 1, are added, respectively, to the four terms of a geometric progression; the…

A: Let the geometric progression is a, ar, ar2, ar3 Then add 7, 9, 8, 1 in the above terms…

Q: Find four numbers that form a geometric progression such that the third term is greater than the…

A: Solving by geometric progressions we have

Q: Find the 57th term of an arithmetic progression when the 1st  term -18 and the common difference is…

A: