2u Fitz GP Question (1 Viewer)

[kazemagic]

Sup,
So for question 23,
I found the ratio for the geometric progression, however it's an irrational number, and the answers had rational numbers in the sequence >.>. I checked my working, and have no idea what I did wrong D:

Any help would be appreciated

Thanks

 

[RealiseNothing]

Summing this gives:



Making the subject:



Also taking the limit:



Solving simultaneously by substituing in 'a':

 

[nightweaver066]

Use (1) to get "a", then solve for thee terms.

 

[D94]

Sum of GP for first 4 terms: a + ar + ar² + ar³ = 65/3 = a(1 + r + r² + r³) = a(1-r⁴)/(1-r)

Sum to infinity: a/(1-r) = 27

Simultaneously, 27(1-r⁴)=65/3

Therefore, r = ±2/3, and a = 81 or 45. However, since the sum is less than both possible values for a, it is likely that r < 0, so we take a = 45.

So the first 3 terms are 45, -30, 20. (and by checking the 4th term, which is -40/3, the sum of these 4 terms does indeed equal 65/3 as stated)

 

[kazemagic]

lol wow influx of answers all at the same time

thanks bros checking ur answers just realised wat my mistake was LOL