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C2 Geometric Series Help!

hey, im stuck on this C2 Geometric Series Question, its Exercise 7F Question 6, pg 107.

The question reads as follows:

The second term of a geometric series is 80 and the fifth term of the series is 5.12:
a) Show that the common ratio of the series is 0.4
Calculate:
b) The first term of the series:
c) The sum to infinity of the series, giving your answer as an exact fraction

Well im stuck on the first bit, completely forgot how to do these, how do i calculate the Common ratio?

Help much appreciated,
Wiz

Reply 1

Dekota

__WiZaRD__

The second term of a geometric series is 80 and the fifth term of the series is 5.12:
a) Show that the common ratio of the series is 0.4
Calculate:
b) The first term of the series:
c) The sum to infinity of the series, giving your answer as an exact fraction

a) 80 = 5.12/r³
... r³ = 5.12/80
... r = ₃√(5.12/80) = 0.4

Edit: Correction :redface:

...

b) ar = 80
... a(0.4) = 80
... a = 80/0.4
... a = 200

c) S = (500 x 0.4)/(1-0.4) = 1000/3

Reply 2

__WiZaRD__

umm, could you explain you got part a) , what, if any, formula did u use?

thx

Reply 3

SunGod87

Correction

b) ar = 80
... a(0.4) = 80
... a = 80/0.4
... a = 200

Reply 4

Dekota

SunGod87

Correction

b) ar = 80
... a(0.4) = 80
... a = 80/0.4
... a = 200

Cheers

Reply 5

SunGod87

__WiZaRD__

umm, could you explain you got part a) , what, if any, formula did u use?

thx

Geometric series is

S = a + ar + ar^2 + ar^3 etc

2nd term ar = 80
5th term ar^4 = 5.12

ar^4 / ar = r^3 = 5.12/80
............... r^3 = 0.064
............... r = 0.4

Reply 6

__WiZaRD__

ahhhhhhhhhhhhhhhhhhhhhhhhhhh,,, thats easy..... Thanx loads!

Reply 7

Dekota

__WiZaRD__

umm, could you explain you got part a) , what, if any, formula did u use?

thx

You have ar = 200, ar² = 80 ... ar^5 = 5.12

so, ar² = 80 and ar^5 = 5.12
... a = 80/r²

substitute this a expression into the other;

... (80/r²)r^5 = 5.12

re-arrange and solve to get r = 0.4