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: 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: 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: 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: 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…

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.