Explanation

In an arithmetic progression (AP), the nth term is given by the formula

Tn=a+(n−1)⋅d

Where:

a is the first term

d is the common difference,

n is the term number.

For the given AP:

First term a=2,

Common difference  d=11−2=9,

We are looking for  n when the term is 290.

Let the given AP contain n terms.

Tn = 290

=> a + (n – 1)d = 290

=> 2 + (n – 1)9 = 290

=> 2 + 9n – 9 = 290

=> 9n = 297

=> n = 33

Thus, the 33 term of the AP is 290.