QUESTION 1
Easy
A student has ₹500 in her savings bank account. She gets ₹150 every month as pocket money. How much money will she have at the end of every month from the second month onwards? Find a linear expression to represent the amount she will have in the nth month.
SOLUTION
1
Identify initial amount and monthly addition
Initial savings \( =\) ₹\(500\)
Monthly pocket money \( = \) ₹\(150\)
Monthly pocket money \( = \) ₹\(150\)
2
Find the amount at the end of each month
End of first month \( = 500 + 150 = 650 \)
End of second month \( = 650 + 150 = 800 \)
End of third month \( = 800 + 150 = 950 \)
So we have 650,800,950,...
End of second month \( = 650 + 150 = 800 \)
End of third month \( = 800 + 150 = 950 \)
So we have 650,800,950,...
3
Derive the linear expression for \(n^{th}\) month
At the end of \(n\) months, she has received pocket money \(n\) times
\( Amount = 500 + 150n\)
\( Amount = 500 + 150n\)
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Final Answer :
Amount at the end of each month: \(650, 800, 950...\)
Linear expression: \(500 + 150n\)
Concept Note
If starting value \( = a\) and constant addition \( = d\), then after \(n\) periods:
\(Value = a + d × n\)