Math Is Fun Forum

beluga

Member

Registered: 2010-06-26

Posts: 8

Sequences

Hi

I dont know how to find the recursive definition of the following

2 + a, 3 +3a, 4 + 5a

And for the next question is there a formula to solve this or do I solve it through trial and error?

The 8th term of an arithemtic sequence is 21 and the 20th term is 105. Find the common difference and the first term.

help is greately appreciated and respected

Cheers

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Sequences

Hi beluga;

And for the next question is there a formula to solve this or do I solve it through trial and error?

In this case there is a formula, sometimes you might have to use trial and error or other methods.

The 8th term of an arithemtic sequence is 21 and the 20th term is 105. Find the common difference and the first term.

Use the formula:

an  = a1  + d*(n – 1)  where a1 is the first term in the sequence and d is the common difference.

when n= 8 then a8 = 21 and (n-1)=7

21 = a1 + 7 d

when n = 20 then a20 = 105 and (n-1)=19

105 = a1 + 19 d

Solve simultaneously:

21 = a1 + 7 d
105 = a1 + 19 d

a1 = - 28 and d = 7

So the sequence is:

-28,-21,-14,-7,0,7,14,21,28,35,42,49,56,63,70,77,84,91,98,105...

a1= -28
a8 = 21
a20 = 105

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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.

DaveRobinsonUK

Member

Registered: 2010-04-24

Posts: 123

Re: Sequences

funny..

I was just thinking about this formula before.

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Can feel it coming together.. Slowly but Surely

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Sequences

Hi Dave;

If you were thinking about this formula then we are in telepathic communication. I know several people here will say such abilities don't exist but we have proven that it does.

Whom do we submit our proof to, Duke University? I smell a Nobel prize, a trip to Sweden, a best seller, a big movie contract. Whom would you like to portray you in the movie? I think Tom Cruise will do a decent job portraying me. Cameron Diaz will be my confused, supportive wife. You know the woman behind the genius?! How will we divide up the money, 50-50 okay with you?

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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.

DaveRobinsonUK

Member

Registered: 2010-04-24

Posts: 123

Re: Sequences

50-50 is SOUND!!

I think I will have Emo Phillips or maybe Sam Elliot and for my dizzy but inspirational wife I will have Sophia Loren, or maybe Audrey Hepburn, who will star as an urn which has a telepathic link to the afterlife (presuming she was cremated, if not old Sam will have his work cut out for him pulling the coffin about town).

Sweden sounds cool too, though we will have to take our own beer. I don't fancy paying $40.00 every time we need more. Although money, should not be a problem with our Nobel coin.

Superb, thats cheered me up no end.

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Can feel it coming together.. Slowly but Surely

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Sequences

Then it is set. We will save a ton if we don't need any attorneys. I will call Tom's agent as soon as we collect the NP. I am looking forward to meeting Sophia Loren. Sam Elliot one of my favorites too. Audrey Hepburn in an urn. Brilliant! Is Martin Scorsese directing okay with you?

First thing first, see you in Sweden! I will bring the beer.

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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.