Find the 11th term of the sequence 1,2,4,8,…

These terms are all powers of 2, so we can write:

Is this sequence geometric or arithmetic or neither: 3,5,9,15 ?

9-5=4
5-3=2
so it is not arithmetic

15/9=5/3

so it is not geometric either
... so neither

Make a conjecture about the next item in the sequence: 1, –8, –17, –26, –35

every term seems to be 9 less than the preceding term :)

1-9=-8
-8-9=-17
-17-9=-26
-26-9=-35
so the next term is probably -44

Suppose Tn= a+(n-1)d is an AP with first term "a" and difference "d". Show that the sequence Un=2^(Tn) is a GP and find its first term and ratio.

take integer k, then




the ratio is

therefore it is geometric with
 and 

Find a recursive rule for the sequence 1, 4, 9, 22,...

Notice the pattern:
2*4+1=9
2*9+4=22
so a reasonable possibility is:

, 

one number is wrong in this sequence what is that number: 1,6,27,64,125,216 ?

6 is not a perfect cube

How do you write an expression for a general term of the following sequence? 2,1,3,0,4,-1,5,...

2 -1
1 +2
3 -3
0 +4
4 -5
-1 +6
5
so that

In a series with common difference 2, 25 is a term in the series. Find the next perfect square in the series?

Since the common difference is 2 (even) and a term in the sequence is 25 (odd), we must find the next odd perfect square after 25 - which is 49 

:)

Is there a pattern for 81,108,144,...?

108/81=4/3
144/108=4/3

looks like it's a geometric sequence with a1=81:




:)

Determine which term of the sequence 3,5,7 is equal to 27

arithmetic sequence...

d=2, a1=3, an=27, n=?


becomes...




so n=13 i.e.
27 is the 13-th term

what is the equation for the sequence 16, 14, 11, 7, 2...

one solution is...

an: 16 14 11 7 2 ....
n: 1 2 3 4 1 ...

Find the general term for the sequence 2/3,3/4,4/5,5/6,…

 Find the general term for the sequence 2/3,3/4,4/5,5/6,…

Solution:

From the terms: 2/3,3/4,4/5,5/6,… we see that the denominator is one unit greater than the numerator. So for the n-th term the denominator will be n+1. This makes out general term: