Math Is Fun Forum

zainyusufazam

Member

From: Canada eh?

Registered: 2021-01-14

Posts: 6

Find sum of n terms in a geometric series using two other sums

hey guys, I've been stuck on this question in my textbook for a little bit; I've checked online but it only gives me sequences, not sums.

my problem is: "In a geometric series, the sum of the first three terms is 304, and the sum of the first six terms is 1330. Find the sum of the first seven terms".

by using the sum of a geometric sequence formula, I've tried equating them both to zero and finding u_1, and then I get u_1 = (1026r - 1026) / (r^6 - r^3)

which gets pretty complicated to substitute. is there something I'm missing?

also, how do I use latex correctly? I read the stickied post and they should be like this <u_1> correct? not sure how to put in a code box. thanks.

Last edited by zainyusufazam (2021-01-14 04:09:21)

irspow

Member

Registered: 2005-11-24

Posts: 1,055

Re: Find sum of n terms in a geometric series using two other sums

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I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

zainyusufazam

Member

From: Canada eh?

Registered: 2021-01-14

Posts: 6

Re: Find sum of n terms in a geometric series using two other sums

oh, that's makes a lot more sense, I never thought about it that way. thanks a lot sir/miss.

irspow

Member

Registered: 2005-11-24

Posts: 1,055

Re: Find sum of n terms in a geometric series using two other sums

No problem, I realized I typed all of that without explanation and wasn’t sure if you followed. If anything didn’t make sense I will fix it.

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I am at an age where I have forgotten more than I remember, but I still pretend to know it all.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Find sum of n terms in a geometric series using two other sums

hi zainyusufazam

Welcome to the forum.

Use of Latex:

If you click on one of irspow's Latex lines you will see the underlying code that was used.  That makes it easier to copy useful commands that others have used.  The Sticky thread also has lots of ideas and you can also search on-line for new commands.  Different forums may have different Latex applications so sometimes you may learn about a command that this forum doesn't support, but that only happens rarely for me.

To send your commands to the Latex interpreter you need to begin and end with two bccode commands.  The begin command is the word math inside square brackets [m... here] Sorry I cannot show it correctly without setting it off.  The end command is similar but with /math inside the square brackets.  If you don't have this second command you'll get an error report when you try to post your work.

This site is also useful for creating Latex: https://latex.codecogs.com/legacy/eqneditor/editor.php

Hope that helps.

Bob

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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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Find sum of n terms in a geometric series using two other sums

hi irspow

While having my breakfast I saw the first post and, keen to have a go, I got out some paper and sketched out a solution.  Then I went to post it and discovered you had already sent exactly the same   I suppose my lesson from this is to read everything before starting an answer.  But the 'work-out' was good for me so why not?  I was a bit worried when I got to the quadratic but when it came out as r = 1.5 I was greatly relieved. Not too complicated but unlikely to allow someone to get the answer just by guesswork.

Best wishes,

Bob

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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

zainyusufazam

Member

From: Canada eh?

Registered: 2021-01-14

Posts: 6

Re: Find sum of n terms in a geometric series using two other sums

hey guys, need help again, bit of a similar question. the problem is:
"In a geometric series, the 3rd term in 45 and the sum of the first 7 terms is 2735.
Find the first term and common ratio r if r (is a part of all integers)"

I know that I need to set up the two equations like this:

I'm just not sure how to solve for them. unlike the last one this is a term and a sum, I'm having trouble finding r again. thanks dudes.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Find sum of n terms in a geometric series using two other sums

hi zainyusufazam

If u1 and r must be integers then the first equation will take you most of the way.

Write 45 as a product of primes.

By inspection you will see only one value of u1 but two values of r are possible.

By evaluating the sum you'll quickly find out which r value works.

Bob

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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

zainyusufazam

Member

From: Canada eh?

Registered: 2021-01-14

Posts: 6

Re: Find sum of n terms in a geometric series using two other sums

you might have seen a deleted post... it seems editing my post wouldn't work.

anyways, I found the answer, but I'm curious to know whether it's possible to find the answer for non integers?

thanks, zain