Suppose that n > 5 and that the numbers t1, t2, t3, . . . , tn−2, tn−1, tn form an arithmetic sequence with n terms. If t3 = 5, tn−2 = 95, and the sum of all n terms is 1000, what is the value of n? (An arithmetic sequence is a sequence in which each term after the first is obtained from the previous term by adding a constant, called the common difference. For example, 3, 5, 7, 9 are the first four terms of an arithmetic sequence.)

Q: Find the generating function for the sequence 1,−2,4,−8,16,….

A: The general expansion of the binomial (1-x)-1 will be, (1-x)-1=1+x+x2+x3+….

Q: Find an  for the sequence 1/1 -22/2x1 +33/3x2x1 - 44/4x3x2x1, +...

A:

Q: Let (a,) be the sequence defined by a¡ = 5 and a, = 2a,-1 – 3 when n > 2. What is a4?

A: Here an be the given sequence which is defined by a1=5 and an=2an-1-3 when n≥2 . We have to find a4…

Q: 5a. In an arithmetic sequence of numbers a1 = -4 and a6 = 46.  Which of the following is the value…

A: Given problems  5a. In an arithmetic sequence of numbers a1 = -4 and a6 = 46. Which of the following…

Q: A sequence has a recursive formulatn = tn-1+nº, tị = 5. Determine t3.

A: The given recursive formula of the sequence is: tn=tn-1+n3...(1) And t1=5

Q: What is the 100th term of a sequence of number in which, for every positive integer x, the sum of…

A: In the given question, concept of summation series is used. Summation Series The total of the series…

Q: Find the first file terms of the following sequence bn=(-1) n(4n-4)

A: To determine: first five terms. Given: bn=(-1)n(4n-4)

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.