Random problems >.<

[Beans]

Aloha! so yep its crazy problem time unfortunately see if you can help? I'm just a smidge stuck but here we go! :roll:

1. Write out the first 5 terms of the geometric sequence {A[sub:10dfugc2]n[/sub:10dfugc2]} in which a[sub:10dfugc2]5[/sub:10dfugc2]-a[sub:10dfugc2]1[/sub:10dfugc2]=60 and a[sub:10dfugc2]4[/sub:10dfugc2]-a[sub:10dfugc2]2[/sub:10dfugc2]= 24

For this one all I have is that a[sub:10dfugc2]5[/sub:10dfugc2] = ar[sup:10dfugc2]4[/sup:10dfugc2] a[sub:10dfugc2]1[/sub:10dfugc2]= a a[sub:10dfugc2]4[/sub:10dfugc2]= ar[sup:10dfugc2]3[/sup:10dfugc2] a[sub:10dfugc2]2[/sub:10dfugc2]= ar and thats pretty much all i could figure out.. i wasn't sure how to set it up.. i got that ar[sup:10dfugc2]4[/sup:10dfugc2]-a=-60 and ar[sup:10dfugc2]3[/sup:10dfugc2]-ar= 24 but don't know how to solve.

2. Find 30
sigma.. 4/n[sup:10dfugc2]2[/sup:10dfugc2]-4 exactly. do not use your calc. show thinking...
n=3

So sorry about the missing sigma E thingy.. :mrgreen: alright here we figured out it was a telescoping series and would equal A/(n-2) + B/(n+2)= 4/((n-2)(n+2)) but again i dunno where to go from here...

3. Last one i swear >.< ... okay this one i just don't know what the pattern is.

1[sup:10dfugc2]2[/sup:10dfugc2]+2[sup:10dfugc2]2[/sup:10dfugc2]+4[sup:10dfugc2]2[/sup:10dfugc2]+5[sup:10dfugc2]2[/sup:10dfugc2]+7[sup:10dfugc2]2[/sup:10dfugc2]+8[sup:10dfugc2]2[/sup:10dfugc2]....97[sup:10dfugc2]2[/sup:10dfugc2]+98[sup:10dfugc2]2[/sup:10dfugc2]

yeppers so here again I just dont know what the pattern would be then i can sum the buddy up quite quickly if i knew that

thanks in advance for trying to read through my mass of confusion!! and thanks much to anyone who can help at all!!

 

[Deleted member 4993]

Aloha! so yep its crazy problem time unfortunately see if you can help? I'm just a smidge stuck but here we go! :roll:

1. Write out the first 5 terms of the geometric sequence {A[sub:43fcjdwb]n[/sub:43fcjdwb]} in which a[sub:43fcjdwb]5[/sub:43fcjdwb]-a[sub:43fcjdwb]1[/sub:43fcjdwb]=60 and a[sub:43fcjdwb]4[/sub:43fcjdwb]-a[sub:43fcjdwb]2[/sub:43fcjdwb]= 24

Find the expression for [a[sub:43fcjdwb]5[/sub:43fcjdwb]-a[sub:43fcjdwb]1[/sub:43fcjdwb]] / [a[sub:43fcjdwb]4[/sub:43fcjdwb]-a[sub:43fcjdwb]2[/sub:43fcjdwb]] and see what do you get out of that.

For this one all I have is that a[sub:43fcjdwb]5[/sub:43fcjdwb] = ar[sup:43fcjdwb]4[/sup:43fcjdwb] a[sub:43fcjdwb]1[/sub:43fcjdwb]= a a[sub:43fcjdwb]4[/sub:43fcjdwb]= ar[sup:43fcjdwb]3[/sup:43fcjdwb] a[sub:43fcjdwb]2[/sub:43fcjdwb]= ar and thats pretty much all i could figure out.. i wasn't sure how to set it up.. i got that ar[sup:43fcjdwb]4[/sup:43fcjdwb]-a=-60 and ar[sup:43fcjdwb]3[/sup:43fcjdwb]-ar= 24 but don't know how to solve.

2. Find 30
sigma.. 4/n[sup:43fcjdwb]2[/sup:43fcjdwb]-4 exactly. do not use your calc. show thinking...
n=3

So sorry about the missing sigma E thingy.. :mrgreen: alright here we figured out it was a telescoping series and would equal A/(n-2) + B/(n+2)= 4/((n-2)(n+2)) but again i dunno where to go from here...

Solve for 'A' and 'B' and write out the expanded series for first few terms

3. Last one i swear >.< ... okay this one i just don't know what the pattern is.

1[sup:43fcjdwb]2[/sup:43fcjdwb]+2[sup:43fcjdwb]2[/sup:43fcjdwb]+4[sup:43fcjdwb]2[/sup:43fcjdwb]+5[sup:43fcjdwb]2[/sup:43fcjdwb]+7[sup:43fcjdwb]2[/sup:43fcjdwb]+8[sup:43fcjdwb]2[/sup:43fcjdwb]....97[sup:43fcjdwb]2[/sup:43fcjdwb]+98[sup:43fcjdwb]2[/sup:43fcjdwb]

Looks like you are missing

3[sup:43fcjdwb]2[/sup:43fcjdwb]+6[sup:43fcjdwb]2[/sup:43fcjdwb]+9[sup:43fcjdwb]2[/sup:43fcjdwb]+12[sup:43fcjdwb]2[/sup:43fcjdwb]+15[sup:43fcjdwb]2[/sup:43fcjdwb]....+ 99[sup:43fcjdwb]2[/sup:43fcjdwb]....

yeppers so here again I just dont know what the pattern would be then i can sum the buddy up quite quickly if i knew that

thanks in advance for trying to read through my mass of confusion!! and thanks much to anyone who can help at all!!