A person is to count 4500 currency notes. Let an denote the number of notes he counts in the nth minute. If `a_1=""a_2="". . . . . .""=""a_(10)=""150` and `a_(10),""a_(11),"". . . . . .` are in A.P. with common difference 2, then the time taken by him to count all notes is (1) 34 minutes (2) 125 minutes (3) 135 minutes (4) 24 minutes

Explanation

To solve the problem step by step, we will analyze the counting of currency notes minute by minute and calculate the total time taken to count all 4500 notes.

### Step 1: Count notes in the first 10 minutes
In the first 10 minutes, the person counts a constant number of notes:
- \( a_1 = a_2 = \ldots = a_{10} = 150 \)

Total notes counted in the first 10 minutes:
\[
...