Question

Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.) 1, 1 3 , 1 5 , 1 7 , 1 9 , ...

Answer 1

The general term for the sequence can be given by the following formula:

`a_n=2\,n+9`

Explanation:

If the sequence you typed starts with first term 11 and continues with terms 13, 15, 17, 19, We understand that the sequence is formed by adding 2 units to the previous term. So we are in the case of an arithmetic sequence with constant difference (d) = 2, and with first term 11.

Therefore, the nth term of this arithmetic sequence can be expressed by using the general form for an arithmetic sequence as:

`a_n=a_1\,+\,(n-1)\,d\\a_n=11\,+\,(n-1)\,2\\a_n=11+2\,n-2\\a_n=2\,n+9`