# what is the pattern in this sequence, 64,48,36,27, (81/4) , (243/16)any help is greatly appreciated(:

rcmath | Certified Educator

The number that got my attention in your sequence was 81/4, this meant that we are going to move from one term to the next by dividing by 4, the following term confirm that theory.

So if we divide 64 by 4, we obtain 16, to get to 48 we have to multiply by 3. Hence the common ratio is 3/4.

Let's check couple more terms to confirm our assumption.

`48*3/4=36 and 36*3/4=27`

Hence you have a geometric sequence with common ratio 3/4, in other words you move from term to the next by multiplying by 3/4.

classsic | Student

Here is how you do sequences the easy way, first is it an arithmetic sequence or geometric? when you add the numbers, they are not equal, but when you divide the 2nd term by 1st, 3rd by 2nd, etc. they have the same ratio so its 0.75 and geometric, ok here is how you solve sequences easily:

﻿64,48,36,27,81/14, 243/16

this is the mother equation for all geometric sequences

T(n)=a(r)^n-1

a = the first term, r = the rate at which it goes up, n= number of terms, t(n) = the value of the nth term

in ur sequence, you are given ur first term of the sequence which is 64, and when u divide every number by the number before it you get the sequence so its the rate: 3/4. and that's all you need, because they didnt ask you to find the value for a specific point. therefore, a = 64, r=3/4, put that in the equation

t(n)=64(3/4)^(n-1)

now if you want to find any term you want you can sub it in to get the value for it, try solving for the 3rd term.

t(3)=64(3/4)^(3-1)

t(3)= 36, and this makes sense because the 3rd term in your sequence is 36.

NOTE: DO NOT USE THIS FORMULA IF IT IS ANY OTHER SEQUENCE, THIS ONLY WORKS FOR GEOMETRIC SEQUENCES!

This is a simplified lesson, hope it helped.