A test question lists the first four terms of a sequence as 2, 4, 6, and 8 and asks for the fifth term. Show that the fifth term can be any real number a by finding the nth term of a sequence that has for its first five terms 2, 4, 6, 8, and a.

Q: Find the sum of the even integers between 21 and 45.

A: Even integers between 21 and 45 are 22,24,26,28,..........44. We can see that difference between two…

Q: The 11th term in the sequence 1/6, -1/2, 3/2, -9/2, ...... can be written as ______?

A: Given geometric series,       16,-12,32,-92,.....

Q: Determine the 15th term of the sequence 3,1,-1,-3

A: A sequence is said to be an arithmetic sequence if the difference between successive term is same.…

Q: A stack of boxes has 17 rows. The bottom row has 40 boxes, and the top row has 8 boxes. Assuming…

A: A stack of boxes has 17 rows. so, number of rows, n=17 Bottom row contains 40 boxes. ∴ a1 = 40 Top…

Q: Write a recursive formula for the sequence 15, 26, 48, 92, 180, .... Then find the next term.

A:

Q: What is the next term in the sequence 100, 83, 68, 55, 44, 35,...?

A: Solution: Given data, 100,83,68,55,44,35...?

Q: Write the explicit formula of the sequence 25, 21, 17, 13

A: Given 25,21,17,13 It is in arthematic series Because it has difference 4 for each number.

Q: Which term of the arithmetic sequence 1, 9, 17, 25, ... is 345? It is the th term.

A:

Q: 2. For the sequence 1, 5, 12, 22, 35, 51, ... i) Use subscript notation to write a recursive formula…

A: The explicit rule for a sequence is used to define the general term of a sequence. For example, the…

Q: Which of the following is the value of x to make x + 1, 4x – 7, 2x + 5,… an arithmetic sequence.

A: We will find the value of x for which the given sequence will be  an arithmetic sequence as…

Q: Derive an expression for the sum of the first n positive even integers.

A: We Use the A.P series. Find The sum of the first n positive even integer.

Q: state the recursive formula that generates the last number in the sequence 1, 2, 3, 5, 7, 11, 15,…

A: The given sequence is 1, 2, 3, 5, 7, 11, 15, 23, 31.

Q: Consider the sequence: 17, 14, 11, 8, ..., find the 26th term of the sequence.

A:

Q: Must the fifth term of the sequence 2 , 4 , 6 , . . . be 10 ? Explain thoroughly.

A: The nth term of a sequence with 1st term a1 and common difference d is given by,

Q: Find the 8th term of the following sequence 6, 12, 24, . . . .

A: series = 6,12,24...   we see that the each value in the series is getting multiplied = 2*previous…

Q: How many terms are there in the sequence 1, 1/2, 1/4, 1/8, ..., 1/16,384? (Answer should be an…

A:

Q: Determine the formula for the nth term of the sequence 2,7,12,17,22?

A:

Q: Find the 8th term in the sequence 18n-36.

A: Put n= 8

Q: Can you use polynomial fitting to find the formula for the nth term of the sequence 4, 7, 11, 18,…

A: No. The sequence of differences is the same as the original sequence so no differences will be…

Q: Find the eigth term of a sequence 3,6,12

A:

Q: Use the recursive formula to find the first 5 terms of the sequence ak+1 = ak-1+ ak a1 = 2, a2 = 3

A:

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.