Sequences/series questions

[tram]

hey guys,

my teacher gave me this whole compliation of spech multiple choice questions and had some real trouble with two sequences/series questions and wondering if anyone could help:

1) 4/3 - 1 + 3/4 - ........... is equal to

   a) 13/12
   b) 25/8
   c) 16/3
   d) 16/21
   e) 1


AND

2) the sum of the first 50 multiples of 7 is:

   a) 350
   b) 8925
   c) 9350
   d) 11025
   e) 7.88 x 10^15


And help would be greatly appreciated

[iNerd]

If the answer to Q2 is (B); 8925 I will put up my workings

[Martoman]

so the first is a sum to infinity.

You know and the common ratio is . a is the first term and r is the common multiple you multiply the previous term by to get the next one.

The sum to infinity is

So





2)

 


The forms an arithmetic series the formula is where is the number of terms, is the first term and is the last term.

In general for n number of terms between there is number of terms. Think about it in the small scale ie how many numbers between 0 and 9? its 10, that is another example is how many numbers from 2 to 7 = This *may* go against your intuition of just 7-2 which is why I am explaining this in detail so you don't get confused. Its because subtraction is a span and doesn't account for the end number.

So to finish this off






Finally

[iNerd]

Okay seems like my answer of 8925 was right and yet I did it differently to the legendary Martoman but then again I'm in Year 10 so I have no idea which way is better

First we identify that it is an arithmetic sequence and then we draw upon the formula: S_n = n/2[2a+(n-1)d] where:
a stands for the first term
d stands for the common denominator difference
n stands for the number of terms

In the question a = 7, d = 7 and n = 50
Sub these values into the formula and you will get 8925; B

EDIT: Martoman pointed out a subtle mistake

[stonecold]

^That is further maths lol... not that I can talk.  I'd still manage to get it wrong.

[tram]

cheers guys, relly appreciate the help (esp you martoman) NOW is see what question one was on about.... i couldn't even recognise the geometric patern lol >.<

[tram]

so the first is a sum to infinity.

You know and the common ratio is . a is the first term and r is the common multiple you multiply the previous term by to get the next one.

The sum to infinity is

So





2)

 


The forms an arithmetic series the formula is where is the number of terms, is the first term and is the last term.

In general for n number of terms between there is number of terms. Think about it in the small scale ie how many numbers between 0 and 9? its 10, that is another example is how many numbers from 2 to 7 = This *may* go against your intuition of just 7-2 which is why I am explaining this in detail so you don't get confused. Its because subtraction is a span and doesn't account for the end number.

So to finish this off






Finally

wow that is the first time sequences has made sense to me.....thx!

Okay seems like my answer of 8925 was right and yet I did it differently to the legendary Martoman but then again I'm in Year 10 so I have no idea which way is better

First we identify that it is an arithmetic sequence and then we draw upon the formula: S_n = n/2[2a+(n-1)d] where:
a stands for the first term
d stands for the common denominator
n stands for the number of terms

In the question a = 7, d = 7 and n = 50
Sub these values into the formula and you will get 8925; B

lol that's probs what i would've done, thx!

[Martoman]

Okay seems like my answer of 8925 was right and yet I did it differently to the legendary Martoman but then again I'm in Year 10 so I have no idea which way is better

First we identify that it is an arithmetic sequence and then we draw upon the formula: S_n = n/2[2a+(n-1)d] where:
a stands for the first term
d stands for the common denominator
n stands for the number of terms

In the question a = 7, d = 7 and n = 50
Sub these values into the formula and you will get 8925; B

The

That thing in brackets, the is the formula for an arithmetic sequence, it is used to find the last term. My method just simplifies it to (a+l) as we have both the first and last terms.

Okay seems like my answer of 8925 was right and yet I did it differently to the legendary Martoman but then again I'm in Year 10 so I have no idea which way is better

First we identify that it is an arithmetic sequence and then we draw upon the formula: S_n = n/2[2a+(n-1)d] where:
a stands for the first term
d stands for the common denominator
n stands for the number of terms

In the question a = 7, d = 7 and n = 50
Sub these values into the formula and you will get 8925; B

and tut tut, i should be in year 9 and I know that its a difference not a denominator  :smitten:  :smitten:

[Linkage1992]

i should be in year 9

what ?! how old are you martoman??