# How do I prove the $n$th term of this sequence is given by $2n-1$ by mathematical induction?

I just started studying mathematical induction, and I'm having a bit of trouble.

The question is simply: The first three terms of an arithmetic sequence are $u_1 = 1, u_2 = 3, u_3 = 5$. Prove that $u_n = 2n - 1$ using mathematical induction.

The questions I've tackled so far only concerned series (like, the sum of n terms in a series). This one got me scratching my head a bit.

Thank you so much!

• Ill-defined. I could put $U_4=108$. – Parcly Taxel Dec 11 '17 at 15:42
• How are the $U_n$ defined? Just listing the first few terms doesn't tell us anything at all about what comes next. – lulu Dec 11 '17 at 15:42
• that's all the question says, really! i guess it means a sequence with 1 as the first term and 2 as the common difference. – Zac Dec 11 '17 at 15:45
• Well, you could add that to your question then. With that information added the claim you want is certainly true. – lulu Dec 11 '17 at 15:48

It is the sequence of odd numbers .i.e an A.P with the first term $1$ and common difference $2$. Let the $n$ th term be $2n-1$. So the $n+1$th term will be $2n-1 + 2 = 2n+1 = 2(n+1) -1$. Thus it is proved by induction.