A man gets ₹60 in first week. and after that every week, he gets ₹3 more than previous week. then how much money will he get on 20th week?

Options

A. ₹1770
B. ₹1620
C. ₹1890
D. ₹1790

Answer

To find out how much money the man will get on the 20th week, we can follow these steps:

### Step 1: Identify the first term and common difference
The first term (amount earned in the first week) is:
- \( a = 60 \) (in rupees)

The common difference (the amount he earns more each subsequent week) is:
- \( d = 3 \) (in rupees)

### Step 2: Determine the number of terms
We need to find the amount earned in the 20th week, so the number of terms (weeks) is:
- \( n = 20 \)

### Step 3: Use the formula for the nth term of an arithmetic progression
The formula for the nth term (\( a_n \)) of an arithmetic progression is given by:
\[ a_n = a + (n - 1) \cdot d \]

### Step 4: Substitute the values into the formula
Now, we can substitute the values we have into the formula:
\[ a_{20} = 60 + (20 - 1) \cdot 3 \]

### Step 5: Calculate the value
Now, we will perform the calculations step by step:
1. Calculate \( (20 - 1) \):
\[ 20 - 1 = 19 \]
2. Multiply by the common difference \( d \):
\[ 19 \cdot 3 = 57 \]
3. Add this to the first term \( a \):
\[ a_{20} = 60 + 57 = 117 \]

### Conclusion
Thus, the amount of money the man will get on the 20th week is:
\[ \text{Amount on 20th week} = 117 \text{ rupees} \]

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