Sequences...

Hello just some questions about sequences:

The sum of the first two terms of an arithmetric progression is 18 and the sum of the first four terms is 52. Find the sum of the first eight terms.

I tried using simultaneous equations to find 'd' but then i couldnt find the sum of the first eight terms....

An arithmetric progression has the first term a and common difference -1. The sum of the first 'n' terms is equal to the sum of the first 3n terms. Express a in terms on n.

Thanks
From John

Reply 1

Loz2402

Neo1

Hello just some questions about sequences:

The sum of the first two terms of an arithmetric progression is 18 and the sum of the first four terms is 52. Find the sum of the first eight terms.

I tried using simultaneous equations to find 'd' but then i couldnt find the sum of the first eight terms....

you've done it right with the simultaneous equations.

after doing the sim. equations you should get a= 7 and d=4.
use the sum to n terms equation:

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

you know a, d and n is 8, so you can do it from there :smile:

and for the second bit, i managed to get a = (n-1) but ive no idea if its right, so i will let better mathematicians answer the question for you lol.

Reply 2

Neo1

OP

4

The answer for part 2 is meant to be 2n - 1/2

But I dont know how to get it..any help pleasee

Thanks
From John

Reply 3

apd35

9

Sn = 1/2N(2a+(N-1)d)

a = a
d = -1
N = 3n

=> Sn = (3n/2)(2a+(3n-1)(-1))
=(3n/2)(2a+1-3n)

by my working

Reply 4

evariste_3086

1

Neo1

An arithmetric progression has the first term a and common difference -1. The sum of the first 'n' terms is equal to the sum of the first 3n terms. Express a in terms on n.

Thanks
From John

first term=a d=-1
Sn=n/2(2a+(n-1)(-1))=n/2[2a-n+1]
S3n=3n/2(2a+(3n-1)(-1))=3n/2[2a-3n+1]
Sn=S3n so
n/2[2a-n+1]=3n/2[2a-3n+1]
2an-n^2+n=6an-9n^2+3n
4an=8n^2-2n
a=2n-1/2

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