SOLUTION: Find the 100th and nth term for each of the following sequences. a. 1,5,9,13,... b.70,120,170... c.1,3,9.... d.8,8^4,8^7,8^10,... e.109+7x3^32,109+8x3^32,109+9x3^32,...

Question 1151584: Find the 100th and nth term for each of the following sequences.
a. 1,5,9,13,...
b.70,120,170...
c.1,3,9....
d.8,8^4,8^7,8^10,...
e.109+7x3^32,109+8x3^32,109+9x3^32,...
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52792)   (Show Source): You can put this solution on YOUR website!
.

            I will solve and answer parts (a), (b) and (c) only.

a) is the arithmetic progression with the first term 1 and the common difference of 4. = 1 + 4*(n-1) = 4n - 3. b) is the arithmetic progression with the first term 70 and the common difference of 50. = 70 + 50*(n-1) = 50n + 20. c) is the geometric progression with the first term 1 and the common ratio of 3. = = .

I just opened your eyes --- you do the rest.

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This problem is about the SIMPLEST properties of arithmetic and geometric progressions.

Learn the subjects from these two groups of introductory lessons in this site

    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions

and

    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
    - Word problems on geometric progressions

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topics "Arithmetic progressions" and "Geometric progressions".

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Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

Find the th and nth term for each of the following sequences.
a. 1,5,9,13,...

=> common difference , arithmetic sequence

the th formula:

so, the th term will be:

b.70,120,170...

=> common difference , arithmetic sequence

the th formula:

so, the th term will be:

c.1,3,9....

=> common ratio , geometric sequence
the th formula:

the th term will be:

d.
8,8^4,8^7,8^10,...
note that exponents of first and second term differ by , same for second and third term, and same for third and fourth term

the th formula:
where =,,....
the th term will be:

=> leave like this because this number is really big

e.
109+7x3^32,109+8x3^32,109+9x3^32,...
I am not quite sure if x represents, I assume multiplication

,,

only difference is in numbers ,,

generally, where = ,,....

the th formula:

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