C2 Maths Helps Geometric Series

2 Questions that im stuck on help appreciated

1). For the geometric series 4/3+8/9+16/27+...... find the least number of terms fro which the sum exceeds 3.92

2). For the geometric series 6+12.6+26.46+... find the greatest number of terms for which the sum does not exceed 1000.

Really stuck tried to use Sn rule then use logs but get stange minus number for n

Reply 1

Albino

You can find r for the first one (if you haven't already) by seeing what number you multiply by to get the next one. Then do the Sum to n for when its >3.92. It's probably an arithmetical error you've made because it looks like you know what to do, if you post working we could have a look :smile:

Reply 2

washdog

Got r to be 2/3 and ended up with 4-8/3^n > 3.92 then solved using logs to get n to be -2.75 Help!

Reply 3

HerrDudelmann

1) a = 4/3
r = 2/3
So we know that Sn = a(1-r^n)/(1-r)
So we say that Sn = 3.92

Therefore, 3.92 = 4/3(1-2/3^n)/1/3

This simplifies to 3.92 = 4(1-2/3^n)

3.92 = 4-4(2/3^n)

0.08 = 4(2/3^n)

0.02 = (2/3^n)

log(0.02) = nlog(2/3)

n = log(0.02) / log(2/3)

n = 9.648...

n = 10

For 2), r = 2.1, use the same method