A person is to count 4500 currency notes. Let an denote the...

A person is to count 4500 currency notes. Let $a_{n}$ denote the number of notes he counts in the $n^{\text {th }}$ minute. If $a_{1}=a_{2}=\ldots \ldots=a_{10}=150$ and $a_{10}, a_{11} \ldots$ are in A.P. with common difference $-2$, then the time taken by him to count all notes is (A) 34 minutes (B) 125 minutes (C) 135 minutes (D) 24 minutes

A person is to count 4500 currency notes. Let $a_{n}$ denote the number of notes he counts in the $n^{\text {th }}$ minute. If $a_{1}=a_{2}=\ldots \ldots=a_{10}=150$ and $a_{10}, a_{11} \ldots$ are in
A.P. with common difference $-2$, then the time taken by him to count all notes is
(A) 34 minutes
(B) 125 minutes
(C) 135 minutes
(D) 24 minutes

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Key Concepts

Arithmetic Progression

An arithmetic progression is a sequence of numbers in which each term is obtained by adding a constant difference to the previous term. This concept is crucial in many contexts where quantities change by a fixed amount, allowing for the prediction and summation of sequence terms.

Arithmetic Series Sum Formula

The arithmetic series sum formula provides a method to calculate the total of an arithmetic progression by using the first term, the last term, and the number of terms. This formula simplifies the process of finding cumulative totals in situations where the rate of increase or decrease follows a linear pattern.

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