How do I find the second term for this sequence: an=2an-1+3 a1=2

Question

I don't really know how to do this, should I just substitute 2 in for n or would that be wrong. 

Answer 1

a_n is the nth term of the sequence.

a₁ is the first term of the sequence, which happens to be 2. If you define a sequence recursively (based on past terms), you need at least one initial term if you have a term like a_n-1, and two if you have a term like a_n-2, etc.

 

Thus a_n = 2 * a_n-1 + 3

 

For a₁ (the second term of the sequence), the term would be 2 * a_2-1 + 3 = 2 * a₁ + 3

 

but we know a₁.  it is defined in the sequence as 2. Thus a₂ = 7

Answer 2

You are given a₁=2;  then a₂=2a₁+3 so a₂=7.  a₃=2a₂+3=17. and so on; each subsequent term is three more than twice the term that comes before it.