Series??? (1 Viewer)

[RHINO7]

This question is giving me the shits!!!!!!!!!!!!!!!! And its an easy question!!!!!!!!!!!!

Find the value of n if the sum of n terms of the series 11+33+99+... is equal to 105251.


Please help!!!!!!!!!

 

[jannny]

I got n = 8.9

or n = 9. But n = 9 gives 108251

 

[RHINO7]

yeah it is 108251, could you please show the working out.

 

[jannny]

Sn = 108251
a = 11 r = 3

Sn = [ a ( r ^n -1) ] / r -1 (sum formula of a GP)

108251 = [ 11 ( 3^n -1) ] / 3-1
216 502 = 11(3^n -1)
210 512 /11 = 3^n -1

[216 502 /11] +1 = 3^n
[ln [ 216502/11 +1 ] ] / ln 3 = n ( take ln of both sides)

n = 9