The sixth term of an arithmetic sequence is 28 and the ninth term is 36.Calculate the sum of the first 14 terms of the arithmetic sequence

Q: The 3rd and 4th terms of an arithmetic sequence are 13 and 18, respectively. What is the 50th term…

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Q: Find the 76th term of the following arithmetic sequence.  13, 17, 21, 25,

A: I have given an answer in step 2.

Q: Find the sum of the first eight terms of the arithmetic sequence in which the fourth term is 9 and…

A: a4=9  &  d=-5 Now consider, a4=9⇒a+3d=9⇒a+3-5=9⇒a=24

Q: Find the sum of the first 94 terms of the arithmetic sequence: -6, –1,4, 9, 14, ...

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Q: Find the 94th term of the arithmetic sequence 25, 31, 37, ...

A: Arithmetic Progression is sequence of numbers where any two consecutive number difference is same.…

Q: Find the 14th term of the given arithmetic sequence. 360, 356, 352, ...

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Q: The second term of a geometric sequence is 6 and the fourth term is 96. Find the possible values of…

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

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

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Q: Find the first term of an arithmetic sequence if the 9th term is 72 and the common difference is 5.…

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Q: The first two terms of the arithmetic sequence are given. Find the missing term. a1 = 6, a, : = 19…

A: Given that first term a1 = 6 and second term a2 = 19 We have to find fifth term a5 = ?

Q: Find the 28th term of an arithmetic sequence where the fourth term is 33 and the tenth term is 15.…

A: Find the common difference, d:

Q: The third term of the arithmetic sequence is 72 and the number of the third term with the fifth term…

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Q: The 7th term of an arithmetic sequence is -37, and the 10th term is -121. Find a,d and the general…

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Q: The eight term of an arithmetic sequence is 216 and the seventeenth term is 369. Find the following…

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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: The third term of a geometric sequence is 5, and the sixth term is -40. Find the eighth term.

A: The nth term of a geometric sequence is given by an=a1rn-1, where a1 is the first term of the…

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

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Q: an arithmetic sequence is 75 and the second term is 11 Find the first term.

A: Here I am providing the handwritten solution

Q: Find the specified term of the geometric sequence. 6th term: 5, 15, 45, . . .

A: sequence is 5,15,45,......... first term, a1 = 5 r = a2/a1    = 15/5     = 3

Q: Find the nth term of the arithmetic sequence with the first term −2, common difference 3, and n =…

A: Given: The first term =-2 Common difference =3 n=10 To determine: nth term of the sequence.

Q: The first term of an arithmetic sequence is -1 and the fifteenth term is 27. Find the sum of the…

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Q: Find the 37th term of an arithmetic sequence whose second and third terms are −4 and 12.

A: Note:-  We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find the sixth term of the geometric sequence whose first two terms are 4 and 6.

A: There are many names if the set of numbers follows a specific pattern to write the terms. They are…

Q: Find the 74th term of the arithmetic sequence –8, 0, 8, ...

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Q: Find the 8th term of the geometric sequence 6, 18, 54, ...

A: A sequence is a function with domain being the set of natural numbers and the range being the set of…

Q: The 5th term of a geometric sequence is 45 and the 8th term is 360. Determine the 20th term.

A: Let the first term of the sequence is a and the common ratio is r. We know that the formula for the…

Q: Find the 100th term of the arithmetic sequence with first term 7 and eighth term 35

A: tn=a + (n-1)d---- Formula a = first term  d = Common difference tn =nth term

Q: Given an arithmetic sequence whose sixth term is 28 and eleventh term is 43, find the sum of the…

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Q: If the third term of an arithmetic sequence is 4 and the seventeenth term is -66​, find eighth the…

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Q: Find the specified term of the geometric sequence. 7th term: 5, 30, 180, ... a,

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Q: Find the sum of the first 23 terms of the arithmetic sequence 4m – 3, –10, .

A: For the terms to be in an AP , the first term should be 4 and not 4m which is a mistake.

Q: The middle term of an arithmetic sequence equals 17, the last term = 32, and the fourth term = 11.…

A: Given middle term = 17 Last term = 32 Fourth term = 11 T4 = a+3d = 11 Middle term = T6 = a+5d = 17…

Q: Find the nth term, the fifth term, and the tenth term of the arithmetic sequence.3, 2.7, 2.4,…

A: Given information: The arithmetic sequence is 3, 2.7, 2.4, 2.1,.... Concept used: The nth term of…

Q: find the first five terms of the geometric sequence.

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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: The tenth term of an arithmetic sequence is 40 and the twentieth term is 30. Find the common…

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Q: Find the sum of the first 97 terms of the arithmetic sequence      9,3,-3,-9,-15

A: Given: The arithmetic sequence as 9,3,-3,-9,-15,... To find: The sum of first 97 terms of the given…

Q: Find the number of terms of the arithmetic sequence. 11, 14, 17, 20, 23, … , 122

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Q: Find the 13th term of the geometric sequence 7, 21,63, ...

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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: Find the 66th term of the arithmetic sequence 25, 10, -5, ...

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Q: Find the 55th term of the arithmetic sequence 8, 24, 40, ...

A: We have to find the 55th term

Q: Find the 9th term of the geometric sequence 8, 32, 128, ...

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Q: Find the sum of the indicated number of terms of the geometric sequence. 5, 10, 20, ...; n = 8

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Q: Find the sum of the first 50 terms of the arithmetic sequence below. - 11. -7, -3, 1, ..

A: Sum of n-terms:            Sn= n22a+(n-1)d ; where a is the first term and d is the common…

Q: If the fifth term of a geometric sequence is 64/27 and the sixth term is 256/81 , find the sum of…

A: Let the G.P. is a, ar, ar2, ar3, . . .arn-1 Sum of first n terms is given by, Sn=a(rn-1)r-1, r>1…

Q: The fourth term of an arithmetic sequence is 11, and the sixth term is 17. Find the second term.

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Q: Determine the sum of the first five terms of the geometric sequence where a = 3 and r=2. ... The sum…

A: The formula to evaluate the sum of n terms of a geometric sequence is Sn=arn-1r-1, if r≠1, where a…

Q: 3. -5, 15, -45,... n = 7

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Q: Find the seventh term of the geometric sequence from the given information. Express the term as an…

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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.