Ramkali saved Rs 5 in the first week of a year and then increased her weekly savings by Rs 1.75. If in the n-th week, her weekly savings become Rs 20.75, find \( n \).
10
Step 1: Recognise the pattern as an AP.
Ramkali's weekly savings form an arithmetic progression (AP):
• First week: Rs 5
• Each week she increases the saving by Rs 1.75
So, first term \(a = 5\) and common difference \(d = 1.75\).
Step 2: Use the nth-term formula of an AP.
The nth term of an AP is given by:
\[a_n = a + (n - 1)d\]
We are told that in the nth week, she saves Rs 20.75. So:
\[a_n = 20.75\]
Substitute \(a = 5\), \(d = 1.75\):
\[20.75 = 5 + (n - 1) \times 1.75\]
Step 3: Solve for \(n\).
Subtract 5 from both sides:
\[20.75 - 5 = (n - 1) \times 1.75\]
\[15.75 = (n - 1) \times 1.75\]
Now divide both sides by 1.75:
\[n - 1 = \dfrac{15.75}{1.75}\]
Compute the division:
\[15.75 \div 1.75 = 9\]
So:
\[n - 1 = 9 \Rightarrow n = 9 + 1 = 10\]
Conclusion: Ramkali's weekly savings become Rs 20.75 in the 10th week, so \(n = 10\).