Join TSR now and get all your revision questions answeredSign up now

C1 - Question for very basic arithmetic sequence - how is "n" this value?

    • Thread Starter
    Offline

    3
    ReputationRep:
    "Find trhe sum of the multiples of 3 less than 100"

    So far, I got: a=3, d=3 but don't know how to work out "n"

    Writing out the sequence, I get 3 +6 +9 +12...+96+99

    I can't work out "n" though to put it in the equation of:

    Sn = n/2 [2a + (n-1)d]

    Looking at the solution bank, i see the value of "n" is [(99-3)/3]+1, which =33, shows that there are 33 terms in the sequence.

    How do you work out that "n" = [(99-3)/3]+1 ?

    I get that the 99 would be the last multiple of 3 less than 100, but I dont get why it is 99-3, and then (99-3)/3 (i dont get why that is divided by 3). I also don't get why there is a +1 at the end.

    Please can you explain?

    Thanks!
    Online

    3
    ReputationRep:
    Let 99 be the nth term.

     u_n = a+(n-1)d

    So  99 = 3+ 3(n-1) and solve for n.
    • Thread Starter
    Offline

    3
    ReputationRep:
    (Original post by NotNotBatman)
    Let 99 be the nth term.

     u_n = a+(n-1)d

    So  99 = 3+ 3(n-1) and solve for n.
    If you let the nth term be 99 to solve it, for Un = a+(n-1)d, wouldn't it be 99 = 3+ 3(99-1)? Because if you let the n in Un be 99, don't you have to let the n in (n-1) also be 99 when solving it?

    If you can leave the "n" in (n-1) just as "n" instead of switching it to 99 like in "Un", why so? Why is this possible? I thought if you substitute 99 for the n in Un that you would also have to substitute the (n-1) for (99-1)?
    Online

    3
    ReputationRep:
    (Original post by blobbybill)
    If you let the nth term be 99 to solve it, for Un = a+(n-1)d, wouldn't it be 99 = 3+ 3(99-1)? Because if you let the n in Un be 99, don't you have to let the n in (n-1) also be 99 when solving it?

    If you can leave the "n" in (n-1) just as "n" instead of switching it to 99 like in "Un", why so? Why is this possible? I thought if you substitute 99 for the n in Un that you would also have to substitute the (n-1) for (99-1)?
    No, n is not the nth term it is the number of terms, which you are trying to find.  u_n is the nth term, whereas  n is the number of terms.

    If it makes it easier, you can use the kth term rather than the nth term and find the sum to k, s_k
 
 
 
Write a reply… Reply
Submit reply
Updated: September 26, 2016
Poll
Which party will you be voting for in the General Election 2017?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.