*30. Formulate Substitute the formula for the nth term of an arithmetic sequence (105) into the formula for the sum of the first n terms of an arithmetic series. In what situation could this new formula be used?

Q: 5. What is meant by the index of a term of a sequence?

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Q: What is the closed form for the infinite geometric sequence beginning  4,2,1,1/2 where the first…

A: Given :The infinite geometric sequence : 4, 2, 1, 12, ..

Q: Find the sum of the terms of the following infinite geometric sequence. 4/5, -1/5, 1/20, ... What…

A: Sum of infinite geometric series is S=a/1-r. see 2nd step.

Q: What is the 5th term of the sequence defined by the formula Tn=2n2−5n+1.

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Q: What is the 46th term in the arithmetic sequence –1.5, –1.3, –1.1, -0.9, .?

A: we have to find out the 46th term

Q: What is the formula for the arithmetic sequence if the sum of the same sequence is given by sn 2n +…

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Q: Clarify the differences between a sequence and a series?

A: Sequence is an array of numbers arranged according to a certain rule. For example,

Q: 3 if it exists. 8 Find the infinite sum of the geometric sequence with a = - 5, r = |

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Q: If the 8th term of an arithmetic series 39 and the 20th term is -33. What is the common difference?

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Q: 41. Find the sum of the first 70 terms of the arithmetic sequence with first term 10 and common…

A: "The student ask for the question number 41, so I am solving the question number 41." Given that,…

Q: 2) Find the sum of the first 100 terms of the arithmetic sequence: 2, 4, 6, 8, 10, 12, ...

A: The arithmetic sequence: 2,4,6,8,10,12,.......

Q: 11. Given that the 5th and 11th terms of an Arithmetic Sequence are 26 and -16, respectively, what…

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Q: What is  the differences between a sequence and a series?

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Q: The first term of a geometric sequence is 8, the second term is 24, & the 3rd term is 72.  What is…

A: The sum of first  n  terms of a geometric series can be calculated using the formula, Sn=a1-rn1-r.…

Q: What is the 46th term in the arithmetic sequence –1.5, –1.3, –1.1, -0.9, ...?

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Q: What is the 8th term of the sequence whose ?th term is defined as ?? = (−1)^n(3n-2)

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Q: What is the 7th term of the geometric sequence defined by the rulean = -3(2)^n-1 ?

A: What is the 7th term of the geometric sequence

Q: The first term of a geometric sequence is 8 and the fourth term is 216. What is the sum of the first…

A: Given, First term = 8 Fourth term = 216

Q: The first term of a geometric sequence is 8, the second term is 24, & the 3rd term is 72. What is…

A: We have to find the sum of the first 12 terms of the geometric sequence where first term is 8,…

Q: 3 What is the sum of the geometric series

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Q: If the common difference of an Arithmetic series is 6 and the 4th term is 10, what is the value of…

A: Sol

Q: 2. The first three terms of either an arithmetic or geometric sequence are given by 6, a, 24. Which…

A: Given,         The first three terms of either an arithmetic or geometric sequence are…

Q: Find the first 4 terms of the sequence defined byf (n) = 1/2n+ n.

A: Consider a sequence an. The first n terms of the sequence are given by: a1, a2, a3,...an

Q: Find the sum, if it exists, of the infinite geometric series that is related to the infinite…

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Q: How would you classify the sequence 0.45,0.045,0.0045, 0.00045,..... A. Arithmetic Series B.…

A: Given sequence

Q: nth term for n = − 5+(n-1)14, where n is a positive integer. What is the value of the tenth term in…

A: we put n=10 in given sequence and find 10th term .see 2nd step.

Q: 2.) Write the general formula for un for the arithmetic sequence 12, 4, –4, –12, ...

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Q: The median of the first five terms of a geometric sequence is 4. The ratio of the first term to the…

A: Let the terms of the GP be a,ar,ar^2,ar^3..

Q: What will be the sum of arithemetic sequence with first term a1=1 and second term a2=24

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Q: 2. If the first term of an arithmetic sequence is 3 and the common difference is 4, what is the 23rd…

A: Topic = Sequence

Q: Find the sum of the first 20 terms of the arithmetic series: 6 + 3 + 0 - 3 - 6 - . . .

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Q: What is the sum of the k terms of the series 5+ 10 +20+40+ ?

A: Given,          The sum of the series 5+10+20+40+.....We know that,          The sum of the series…

Q: . How would you classify the sequence 28, 21, 15, 10,6, B. Geometric Series A. Arithmetic Series D.…

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Q: If the 100th term of an arithmetic sequence is 902, and its common difference is 9, then its first…

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

Q: If the first term of a geometric sequence is 0.9 and its ratio is 0.2, what is the sum of the first…

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Q: What is the n^th term of the following sequence 1,4,7,10

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Q: 6. Find the indicated nth term of the geometric sequence. 22th term : 8, 32, 128, ...

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Q: Find the indicated term of the sequence by finding the explicit formula for the nth term. 9. 100th…

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Q: What will be the nth term of the geometric sequence with first term a1=4, a2=8 and n = 4

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Q: The sum of the first five terms of the arithmetic sequence is -5 and the sixth term is -10. The sum…

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Q: A town has a population of 5000 persons, but is expected to grow by 2% every year. (i) What would…

A: Solution: From the given information, the town has a population of 5000 persons. But it is expected…

Q: What is the sum of 0.34343434, .... , and 4.4111... (Under Geometric Sequence Topic

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Q: Select a formula for the general term ³ of the sequence, assuming that the patt of the first few…

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Q: Find the first 6 terms of the sequence defined byf (n) = 2n + 3.

A: Given, f(n)=2n+3

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: (a) If all your ancestors were distinct, what would be the total number of your ancestors for the…

A: Given that, you have two parents, four grand parents and eight great grand parents. (a) In the first…

Q: Find the indicated nth partial sum of the arithmetic sequence. 6.3, 6.1, 5.9, 5.7,. . .,   n = 13

A: Given arithmetic sequence is  6.3, 6.1, 5.9, 5.7,...... we are given with arithmetic sequence, so…

Q: 1. What is the ninth term of a harmonic sequence if the first three terms are 111 2'6'10 2. Find the…

A: This is the problem of counting and series and finite math.

Q: certain bacteria triples in amount everyday. If there are 100 bacteria presemt during day 1, what…

A: To calculate total count of bacteria after 10 days.