# Math Help - Can any 1 help on SEQUENCES?

1. ## Can any 1 help on SEQUENCES?

Hi all i have these two problems that have been bothering me , any 1 know how to solve it please

1. A string vibrates 30mm in the first oscillation and subsequently 90 % of its previous value in each succeding ocsillation. How many oscillation will it take before the vibration falls below 10mm and how far will it have vibrated in this time?

2. The sum of the first n terms of a geometric series is

1/3 - 2^n/3^n+1

Find
ii) The first term
ii) the second term
iii) the common ratio

2. 1. You have $a = t_1 = 30$ and each time you have $90\%$ of your previous value, so the common ratio $r = 0.9$.

You should know that $t_n = ar^{n-1}$, so $t_n = 30\cdot 0.9^{n-1}$.

So if $t_n < 10$ then that means

$30\cdot 0.9^{n-1} < 10$.

Solve for $n$, you will need to use logarithms.

3. 2.

i) a_1=? (put n=1 in your sum formula)
ii)a_2=? (put n=2 into sum formula, but you get the sum of two elements a_1+a_2, what you should do? hint: use i) )
iii)q=a_(n+1)/a_(n)=a_2/a_1