Predict the general term or nth term an for the sequence 579

Predict the general term, or nth term, a_n, for the sequence.

5,7,9,11,13,..

a_n=

Please show how to solve this

Solution

Here, the first term in the sequence 5, 7, 9, 11, 13, ..... is \'5\'

Let us call this term a₁.

thus a₁ = 5

also, we see that the common difference between two neighbouring terms is 2.

that is, d = 7 - 5 = 2

and d = 13 - 11 = 2

to get the 2nd term of the sequence, we add 2 to the first term a_1. Similarly, to obtain 3rd term of the sequence, we add 2 twice to the first term a₁.

therefore if we keep adding 2 to the first term of the sequence (n - 1) times then we will obtain the n^th term of the sequence.

that is, a_n = a₁ + (n - 1)d

so, a_n = 5 + (n - 1)2

=> a_n = 5 + 2n - 2

=> a_n = 3 + 2n

one can check for the validity of this answer by substituting the value of n.