( i understand also that the number is multiplied by 3 each time, yet i don"t recognize just how to find the nth term :/)

AND for: 1, 3, 15, 61, 213


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The "nth" term can be anypoint, depending upon n"s worth. So we must compose an equation valid for any type of value of n.

You are watching: What is the next number in the sequence? 3….9….27….81….

Let"s watch... we know the first term, 3, and the second is 9. You"ve detailed that each successive term is 3 times greater than the one before. Because we start through 3, eextremely term have the right to be written as a number of 3s:

first term: 3 = 3

second term: 9 = 3 * 3

third term: 27 = 3 * 3 * 3

fourth term: 81 = 3 * 3 * 3 * 3

You"ll note that for each term, the number of threes multiplied together equates to the ordinal position of the term. So for n=4, we have to multiply four threes together. This have the right to be written utilizing a base and exponent to represent the variety of threes we are multiplying.

For each term n, the answer is 3n, or three raised to the n-th power. The n-th term is determined by multiplying n threes together.


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