Question

each successive term of the sequence 1, 3, 7, 15, 31...is obtained by adding one to twice the previous term. the 10th term is 1023. what is the value of the 9th term?

Answer 1

511

Explanation:

We have that the sequence is given as follows according to the statement:

`a_n=2\cdot(a_(n-1))+1`

Therefore, to calculate the value of the 9t0 term, we can do the following:

`\begin{gathered} a_(10)=2\cdot a_9+1 \\ a_(10)=1023 \\ \text{ replacing and solve for }a_9\colon \\ 1023=2\cdot a_9+1 \\ 2\cdot a_9=1023-1 \\ a_9=(1022)/(2) \\ a_9=511 \end{gathered}`

The 9th term is 511