"If the second term of a geometric progression is 6 and the fourth term is 54, how many terms must be taken for their sum to equal 242?"

Q: How many terms of the geometric sequence 1÷27 ; 1÷9 ; 1÷3 ;....yield a sum of 364÷27?

A: The solution for the above question is as shown below.

Q: In an arithmetic sequence, the first term, a1, is equal to 9, and the third term, a3, is equal to…

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Q: There are 7 terms in a geometric progression such that the first term is 4 while the fourth term is…

A: Given, There are 7 terms in a geometric progression First-term of geometric progression = a= 4…

Q: The sums of nth term of three arithmetical progression are S,,S, and S,.The first term of each is…

A: We will solve the problem

Q: The first term of an Arithmetic Progression is 15 and the last term is 85. If the sum of all terms…

A: As per our guidelines we are supposed to answer only first question please repost other parts in the…

Q: In a sequence of 12 numbers, each term, except for the first one, is 12^11 less than the previous…

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Q: (a) The first term of a particular arithmetic progression is a natural Number, and the last term is…

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Q: The 5th term of a geometric sequence is 1229 and the 13 th term is 206. Write an equation involving…

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Q: The ratio of three numbers is 2:5:7. If 7 is subtracted from the second number, the resulting…

A: Explanation of the answer is as follows

Q: find the sum of the first 15th terms in the given progression of 1/2,1/4, 1/6……… (complete…

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

A: In the question it is asked to calculate the value of first and thirteenth term of AP.

Q: The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the…

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Q: The first term of a geometric sequence is  1536 and the common ratio is 1 /2 . Which term of the…

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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: Topic - arithmetic progression  And geometric Progression First term is 175 and last term is 205…

Q: (a) The 1st term of an arithmetic progression is 17 and the 6th term is 62. Determine the 8th and…

A: We have to answer questions on Arithmetic progression.

Q: A Geometric Progression has the following terms: 5000, 5550, ... . Which term in this sequence would…

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Q: is 28 and the 7th term is 448, then find the 9th term of this GP. Show all steps.

A: Introduction: A geometric progression is a sort of progression in which each term has a fixed ratio…

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: 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: The 4th term of a geometric progression is and the seventh 16 term is 81 20 find the geometric…

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Q: 4) The first term of an AP is 3 and the last term is 17. If the sum of all terms is 150, what is the…

A: see the attached image below

Q: ifth term and twice the third of an arithmetic progression equals the twelfth term. if the seventh…

A: Introduction: Arithmetic progression is a progression in which each term following the first is…

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

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Q: A machine is driving a 5.5 foot post into the ground. The first hit drives the post 18 inches into…

A: If machine run forever, post will driven into the ground by 48inch.

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

A: S∞=35r=25a=?

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

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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: What is the 8th term of geometric progression if the 4th term is 189 and the sixth term is 1701?

A: In geometric progression, terms are obtained by multiplying the previous term with the same number,…

Q: 7. If the 3rd term of an arithmetic progression is 4 and the 9th term is -14, solve for the common…

A: Given: The 3rd term of an arithmetic progression is 4 and the 9th term is -14. Required: To find the…

Q: How many terms of the arithmetic sequence 20, 18, 16.... must be added so that the sum will be -100?

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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: In a sequence of numbers, the first term is x and each term thereafter is twice the previous term.…

A: solution is given below

Q: The sum of three consecutive terms of a geometric sequence is 104 and their product is 13824.find…

A: Let the three consecutive terms of a geometric sequence be a, ar, ar2.

Q: In a certain arithmetic progression the 20th term is 32 and the common difference is 3 find the…

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Q: There are three numbers in geometric progression whose sum is 26. If the first is increased by 2,…

A: The arithmetic and geometric progressions are two important rule that terms of a sequence follow to…

Q: 1) In an AP the 9th Term is 73 and the 4th Term is 43. What is the sum of the first twenty terms?…

A: Formula: The nth term in the arithmetic progression is: an=a1+n-1d where a1 is the first term and d…

Q: A. Find the sum of the first 20th terms of the given arithmetic progression if the first term is 5…

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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: 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: 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: The sum of first 6 terms of an arithemetic progression is 42 the ratio of its 10th term to its 30th…

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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 the sum of the first 20th terms of the given arithmetic progression if the first term is 5 and…

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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

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.