The problem describes an arithmetic progression in which a person's income starts at ₹300,000 in the first year and increases by ₹10,000 every year for the next 19 years. We are tasked with finding the total income over 20 years.

Step 1: Formula for Sum of Arithmetic Progression

The formula for the sum $S_n$ of the first $n$ terms of an arithmetic progression is: $S_n = \frac{n}{2} \times \left( 2a + (n-1)d \right)$ Where:

• $a$ is the first term,
• $d$ is the common difference,
• $n$ is the number of terms.

Step 2: Assign Known Values

• First term $a = 300,000$
• Common difference $d = 10,000$
• Number of terms $n = 20$

Step 3: Plug in Values

$S_{20} = \frac{20}{2} \times \left( 2(300,000) + (20-1)(10,000) \right)$ Simplify the terms: $S_{20} = 10 \times \left( 600,000 + 190,000 \right)$ $S_{20} = 10 \times 790,000$ $S_{20} = 7,900,000$

Final Answer:

The total income over 20 years is ₹7,900,000.

Would you like a detailed breakdown of any part of this solution or additional questions answered? Here are related queries:

1. What is the income in the 10th year?
2. How to calculate total income if the increment were ₹15,000 per year?
3. How does the formula for arithmetic progression work?
4. What would be the total if the initial income started at ₹400,000?
5. How can this problem be modeled graphically?

Tip: Always double-check your formula inputs, especially for sequences like arithmetic progressions.