Write an expression for the most apparent nth term of the sequence. Assume that n begins with 1. 3,7,11,15,19... can someone please tell me if I'm correct?   3,7,11,15,19...= 4n - 1 1/3,2/9,4/27,8/81,... (1^(n - 1))/3^n

Expert Answers

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1) Your first answer is correct.

You have an arithmetic sequence with the common difference 4, and first term 3.

`a_n=3+(n-1)*4=>a_n=3+4n-4=4n-1`

2) Your answer is incorrect.

we notice that the numerators are 1,2,4,8,... in other words 2^0,2^1,2^2,2^3,... Thus the nth term should have numerator 2^(n-1). You got the denominator part correct.

Hence `a_n=(2^(n-1))/(3^n)`

 

 

 

 

 

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