The first three terms of an arithmetic progression are h - 2, 5k - 1, 2h + k, ... Express k in terms of h.

Q: The sum of the first 17 terms of an arithmetic progression is 187. If the 17th term is -13, what is…

A: sum of first 17 term is 187 and 17th term is -13

Q: Find the first five terms of the arithmetic progression whose fourth and eleventh terms are 30 and…

A: Given the fourth and eleventh terms of an arithmetic progression is 30 and 107

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: 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: 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 an Arithmetic Progression the 17th term is 3 times the 6 th term. If the 11 th term is 63, what…

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Q: The third term of an AP is four times the sixth term and the sum of the first ten terms is 150. Find…

A: The solution is given by using formulaes for nth term and sum of n terms as below:

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 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: 3. Find the 94th term of the arithmetic progression whose fourth term is 3/3 and whose 47th term is…

A: Given, a4=33a47=463

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

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Q: Find all arithmetic progressions with a difference 10 formed of more than 2 primes.

A: We have to find all arithmetic progressions with a difference 10 formed of more than 2 prime.

Q: Let a, be a geometric progression, defined as a1 = 2(first term) and common ratio r = -2. Find the…

A: Find the sum of first 10 terms

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: The sum of two consecutive terms in the arithmetic sequence 1​, 4​, 7​, 10​, ... is 299​; find these…

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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: Find the sum of the first 8 terms of the geometric progression: 2, 4, 8, 16,... -. What is the sum…

A: The geometric progression is a sequence that is formed by multiplying a constant term to the…

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 first term of a geometric progression is 40 and the fourth term is 5. Find the sum to infinity…

A: We have to find sum of infinity of the geometric progression if first term of a progression is 40…

Q: Find the seventh term of the arithmetic progression x, x+y, x+2y,....

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Q: 2) Find the 10th and 20th terms of the geometric progression with first term 3 and common ratio 2.

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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: 10. (a) Explain why the first n natural numbers, {1. 2, 3, -, (n-1), n}, is an arithmetic…

A: 10. In this question, we need to show that the sum of first n natural numbers is 12nn+1 and then we…

Q: Find the sum of the first 10 terms of the geometric progression 2, 4, 8, 16 …

A: To find the sum of the first 10 terms of the geometric progression 2, 4, 8, 16 ...

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: The 3rd term of an arithmetic progression is 4 and the 9th term is -14. Find the sum of the first…

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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: If the 3rd term of a geometric progression is 28 and the 7th term is 448, then find the 9th term of…

A: Use the formula for the nth term of a Geometric Progression (GP).

Q: Find the sum of the first 12 terms of an arithmetic progression whose 7th term is 5/3 and with a…

A: General terms  of  an A.P. is  = a ,  a+d , a+2d , a+3d ,a+4d , a+5d , a+6d  and so on ...... Where…

Q: 1) Write down the 10th and 19th terms of the arithmetic Progressions 8, 11, 14, . ..

A: A sequence an Is said to be arithmetic if a2-a1=a3-a2=...=an-an-1=d (say) Then nth term of the…

Q: What is the sum of the first 50 terms in an arithmetic progression if the 3rd term is 10 and the…

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Q: f 3rd term and 9th term of an arithmetic progression are 4 and - 8 respectively which term of the…

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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: (a) The 1st term of a geometric progression is 4 and the 6th term is 128. Determine the 8th and 11th…

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Q: If the 3rd term of a geometric progression is 52 and the 7th term is 832, then find the 16th term of…

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Q: The third and eighth term of an Arithmetic progression are 470 and 380 respectively. Find the first…

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Q: The first term of a geometric progression is 12 and the fifth term is 55. Determine the 8th and the…

A: Given information: The first term of a geometric progression is 12 and the fifth term is 55. Concept…

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: the sum of the first n terms of an arithmetic progression is given by Sn=3n2 - n i) common…

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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

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

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

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