Series help! (1 Viewer)

[jeongsook]

Hi im struggling with series and sequences that begin like this:

if 26+a+b+c+d+11+.... is an arithmetic series, find a, b, c, and d..

Find the sum of the positive integers less than 100 which are not divisible by 5

Thank you in advance...

 

[FinalFantasy]

a-26=11-d
b-a=a-26
b=2a-26
c-b=a-26
c=b+a-26=3a-52
d-c=a-26
d=c+a-26=4a-78
now a+d=37
so a+4a-78=37
a=23
b=2a-26=20
c=3a-52=17
d=4a-78=14

I think thats right unless i made an error somewhere

 

[FinalFantasy]

forgot what series and sequences is about so can't help w\ 2nd part=P, i barely even learnt it..
just did that 1st part out of logic :\

 

[|Axis_]

Hey, I thought the HSCs over already.. hehe, i like FinalFantasy's method! But maybe this method is easier:


if 26+a+b+c+d+11+.... is an arithmetic series, find a, b, c, and d..

Let x be the difference between successive terms. Write:
26 + 5x = 11
so x = -3

Then a = 26 + 1(-3)
b = 26 + 2(-3)
c = 26 + 3(-3)
d = 26 + 4(-3)


Find the sum of the positive integers less than 100 which are not divisible by 5

This is the same as: Sum( +ive integers <100 ) - Sum( +ive integers <100 divisible by 5)
The 1st sum is 1 + 2 + 3 + ... + 99 = (99/2)(2 + 98)
The 2nd sum is 5 + 10 + 15 + ... + 95 = (19/2)(10 + 5(18))

The answer then should be (1st sum) - (2nd sum).

 

[jeongsook]

Thanks for your consideration guys ^^