Given the first three terms of a geometric series is shown below.  k , 6 , 5k+8 where ? is a constant. i) Prove that one of the possible values of k is 2. Then find the other value. ii) If k = 2, find the sum of the first 10 terms of the series.

Q: Determine whether the statement is true or false. If the statement is false, make the necessary…

A:

Q: State next to each series if it is geometric or not geometric. For those that are geometric, find…

A:

Q: In series A, the first term is 2, and the common ratio is 0.5. In series B, the first term is 3, and…

A: For the series A:                                  First Term is :=2                  Common…

Q: The sum of an infinite geometric series is 5. If the first term is 4, what is the value of the…

A:

Q: Write out the first few terms of the geometric series, > , to find a and r, and find the sum of the…

A: Given geometric series: ∑n=0∞3x-44n substituting n=0, 1, 2 , 3.. will give first term(a), second…

Q: a. Find the common difference and number of terms in the series 3.5+10+...+647 and hence find the…

A:

Q: The sum of n terms of a certain series is 4" – 1 for all values of n Find the first three terms and…

A:

Q: The sum of the first n terms of a series is given by S, = 2n² +n. (a) Find an expression for the nth…

A:

Q: If it exists, what is the sum of the series? 11 15 11 (Give an exact answer in the form of a…

A: Given series

Q: If the ratio of the geometric series Ir|<1, then it is converge and it's sum is:

A:

Q: Write the first four terms of the infinite geometric series with first term a = 5 and common ratio r…

A:

Q: The third and fourth terms of a geometric series are 6.4 and 5.12, respectively. Find (a) the common…

A: The general term of the geometric series is given by arn-1 where a is the first term and r is the…

Q: 1. What's an infinite series that can "sum" to 1?

A:

Q: Σ, 6 what is the value of the series

A: Sum of the infinite terms of geometric series whose first term is  'a' and common ratio is 'r' is…

Q: fourth

A: We will solve the problem.

Q: The sum of the first four terms of a geometric series is 170.04. The common ratio is 0.3 Find the…

A:

Q: From the given series , Find the 34th term

A: The given series should be 34,62,90,118 We can see that the series is in arithmetic sequence. Here,…

Q: State whether the series is geometric or not geometric, and give a reason. (ii) If the series is…

A: Series convergence

Q: if the 8th term in an arithmatic series is 39 and the 20th term -33 what is the common difference

A:

Q: - , How many terms of the series do we need to add in order to find the sum to the inaicated…

A: The approximation of a series is obtained by substituting large values of the variable. Very large…

Q: If the third term in the geometric series Larn is -108 and the sixth term is 32 then the ratio of n…

A: We have to find the ratio of given geometric series.

Q: The first three terms of a sequence are given by 5x + 8, -2r+1, x-4 (a) When x= 11, show that the…

A: Given problem:- The first three terms of a sequence are given by   5x + 8, - 2x + 1, x - 4   (a)…

Q: The partial sum in the arithmetic series with first term 17 and a common difference 3 is 30705.

A: a=17, d=3 and Sn=30,705 The formula for the partial sum of the arithmetic sequence is, Sn=n22a+n-1d…

Q: How many terms of the series 54 , 51 , 48 ..... be taken so that thier sum is 513 ? Explain the…

A:

Q: The sum of the first three terms of a geometric series is 52, and the common ratio is r = 3. Find…

A: Given: The sum of the first three terms of a geometric series is 52 S3=52 Common ratio is r = 3…

Q: If the first term and nth term of a series are -3 and 10+2an-1  Then find second third and fourth…

A:

Q: Determine how many terms of the following convergent series must be summed to be sure that the…

A:

Q: 43.

A: Sum of geometric series problem.....

Q: Find the value of x for which the given geometric series converges. Also, find the sum of the…

A:

Q: ind the sum of the infinite geometric series or show that the sum does not exist: 9 + 3+1++....

A: We know that sum of infinite geometric series with 1st term 'a' and common ratio 'r' is given by…

Q: Find a formula for the nth term of the sequence  3/6, 4/7, 5/8, ...   Assume the series begins at…

A: Given: The sequence is 3/6, 4/7, 5/8, ...

Q: A geometric series has 7 terms. It begins with 350 and decreases by15% for each term. What is the…

A: Given data is : A geometric series has 7 terms. Number of terms n=7  First-term a is 350 and each…

Q: State whether the series is geometric or not geometric, and give a reason. (ii) If the series is…

A: In the question we have to find whether series is convergent or not also geometric or not.

Q: 7n2 + 2n (b) Does the series, converge or diverge? If it converges, what does 3+11n2 + 5n n=1 it…

A:

Q: Is an arithmetic series, S40 = 1900 and U40 = 106. Find the value of the first term and the common…

A:

Q: Consider the infinite geometric series with first term and common ratio . Find the sum of the…

A: I have Provided this answer in step-2.

Q: find the sum of the series 1 as a geometric series, differentiate both sides of express n=0 pect to…

A:

Q: the sum if convergent. 4) 2-6+18-54...

A: In this question, we will evaluate this series and test for convergence.

Q: Find the sum of n terms of the series whose nth term is (i) 2n? - 3n + 5 (ii)n? + 2"

A:

Q: use thE formula for the sum of a geometric series to find the sum or state that the series diverges

A:

Q: find the sum of each geometric series if it exists. Explain why the sum exists,or does not exist.…

A:

Q: How many terms of the series , do we need to add in order to find the sum to the accuracy…

A: Solution Given ∑n=1∞(-1)n-1n2we need to find the how many series do we need to add in order to…

Q: An infinite geometric series has a first term a1 15 and a sum of 45. Explain how you can use the…

A: Given an infinite geometric series with first term a1=15 and sum S=45 Let r be the common ratio of…

Q: The first three terms of a geometric series are 2x, x-8, and 2x+5 respectively. Find the possible…

A: If a, b, c are in geometric progression, then it can be written that ab=bc .

Q: Please answer number 1. find the first four terms and the (n+1)st term of the series whose nth term…

A: Given that: (-1)n-1xn(2n)!     NOTE: As per our answering guidelines, we can only answer 1 question…

Q: The first and sixth term of an arithmetic series are 3 and 33 respectively.The third term and the…

A:

Q: The sum of the first 4 terms of a geometric series is 15 and the sum of the next 4 terms is 240.…

A: Here we will find the positive constant ratio,

Q: A geometric series will sometimes have an infinite sum that is a real number. True O False

A: