mathematics!!!!?

Question

please solve these questions for me.. thanks


geometric progression

calculate the number of terms of the geometric progression 1/4,1/12, 1/36....,1/324.


for the geometric progression 500,100,20... which term will be less than 1/10 for the first time?


how many terms of the geometric progression 48,24,12,...must be equal for the sum to be equal to 95/1/4?


the third term and the 6th term of a geometric progression are 27 and 8. find the second term.

the amount if the insurance coverage for a newly bought imported car in the year 2001 was rm120 000. the amount insured for each of the following years will decrease by 5% as compared to d previous year. calculate the amount insured for the year 2009.

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sum of infinity of a geometric progression

the second term n the 4th term of a geometric prgression are 20 and 12/4/5 respectively. if all the terms are positive, find the sum to infinity.

Answer 1

1) 1/4, 1/12, 1/36, .... , 1/324

To calculate the number of terms, we just need to know what term
1/324 is.

In this geometric progression, a1 = 1/4, and r = (1/12) / (1/4) = 1/3.

Therefore,
a[n] = (a1)r^(n - 1)

We just need to solve for n, letting a[n] = 1/324, a1 = 1/4, and
r = 1/3.

1/324 = (1/4)(1/3)^(n - 1)

Multiplying both sides by 4,

4/324 = (1/3)^(n - 1)

Reducing the fraction,

1/81 = (1/3)^(n - 1)

We can actually solve this without using logarithms, since 1/81 is equal to (1/3)^4.

(1/3)^4 = (1/3)^(n - 1)

Now, equate the exponents.

4 = n - 1, which gives us
n = 5. There are 5 terms in the geometric progression.

2) 500, 100, 20, .....

For this series, a1 = 500, and r = 100/500 = 1/5. That makes the formula
a[n] = (a1)r^(n - 1)
a[n] = (500)(1/5)^(n - 1)

We want to solve for a[n] such that a[n] < 1/10, so we solve the inequality

a[n] < 1/10
(500)(1/5)^(n - 1) < 1/10
Dividing both sides by 500, we get

(1/5)^(n - 1) < 1/5000

Take the antilog of both sides,

n - 1 < log[base 1/5] (1/5000)

Solve this inequality for n, take the nearest integer.

Answer 2

I am not really good at this but i give it a try let's see. I know 4 sure d first one is 1/108 (cuz u multiply everyone by 3) I think d next one is 5 (cuz u divide each one by 5) don't kno bout d rest sorry but i made myself feel good cuz i never did dis in school but i shocked myself by answering d first 2 questions BUT d first guy cud b right it seems like he knows what he's tlkin about goo luck