Math Is Fun Forum

macy

Guest

Sequence and series

Is there any one can help me these questions please

1. The sum of the first n terms of a particular sequence is given by Sn = 17n − 3n2.
a    Find an expression for the sum to (n − 1) terms.
b    Find an expression for the nth term of the sequence.
c    Show that the corresponding sequence is arithmetic and find a and d.

2. Show that the sum of the first 2n terms of an arithmetic sequence is n times the sum of the two middle terms.

thank you buddies

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Sequence and series

Hi;

Not sure what you are asking because your notation ( and I am seeing a lot of this ) is confusing. n2 is n^2?

a) S(n-1) = 17(n-1) − 3(n-1)^2

The sequence is:

S = 14,8,2,-4,-10, ...

You can now do the rest.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Sequence and series

hi Macy,

1. The sum of the first n terms of a particular sequence is given by Sn = 17n − 3n2.
a    Find an expression for the sum to (n − 1) terms.

I see bobbym has done this part for you.  Because the formula has 'n' all you need to do for any questions like this is to replace the 'n' with 'n-1'  .

b    Find an expression for the nth term of the sequence.

Now you have the answer to (1) you can subtract the 'n-1' result from the 'n' version.  The difference will be the nth term

c    Show that the corresponding sequence is arithmetic and find a and d.

Then put n = 1 and you'll have 'a' straight away.

Replace 'n' with 'n-1' in the nth term formula and you'll know the (n-1)th term.

Subtract and you'll have the difference.  If there's an 'n' in that answer then it is not an arithmetic sequence.  If you just get a number then it is; and that number is 'd'.

2. Show that the sum of the first 2n terms of an arithmetic sequence is n times the sum of the two middle terms.

You'll need to write down a formula for the sum of 2n terms.

Then you'll need formulas for those middle terms.  The first will be the nth term and the second will be the (n+1)th term.

Add them and times by n.  Simplify to show the two formulas are the same.

That should do it!

Post back if you need more help.

Bob

Last edited by Bob (2011-09-01 19:34:36)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Macy

Guest

Re: Sequence and series

Thank you all. I have worked out from your hint
Have a good weekend!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Sequence and series

Hi;

Is it Friday? I thought it was Thursday.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.