Question

If a_1=2 and a_n=2a_n-1 find the first five terms of the sequence

Answer 1

a1 = 2, a2 = 4, a3 = 8, a4 = 16, and a5 = 32

Step-by-step explanation:

Given the first term and the nth term of the sequence as;

`\begin{gathered} a_1=2 \\ a_n=2a_(n-1) \end{gathered}`

Since the first term is given already to be 2, let's go ahead and find the 2nd term;

`\begin{gathered} a_2=2a_(2-1) \\ a_2=2a_1 \\ a_2=2\ast2 \\ \therefore a_2=4_{} \end{gathered}`

The 3rd term will be;

`\begin{gathered} a_3=2a_(3-1) \\ =2a_2 \\ =2\ast4 \\ \therefore a_3=8 \end{gathered}`

The 4th term can be found as follows;

`\begin{gathered} a_4=2a_(4-1) \\ =2a_3 \\ =2\ast8 \\ \therefore a_4=16 \end{gathered}`

The 5th term can found as follows;

`\begin{gathered} a_5=2a_(5-1) \\ =2a_4 \\ =2\ast16 \\ \therefore a_5=32 \end{gathered}`