Ramkali saved ₹ 5 in the first week of a year and then increased her weekly savings by ₹ 1.75. If in the nth week, her weekly savings become ₹ 20.75, find n.
n = 10
Explanation
This is a direct application of the nth term formula of an Arithmetic Progression. The problem describes a sequence where Ramkali's savings increase by a fixed amount each week, which is the definition of an AP. The student needs to identify the first term, common difference, and apply the formula aₙ = a + (n-1)d to find the value of n.
Solution Steps
Step 1: Identify the AP parameters: First term (a) = ₹ 5, Common difference (d) = ₹ 1.75, nth term (aₙ) = ₹ 20.75
Step 2: Apply the nth term formula: aₙ = a + (n-1)d
Step 3: Substitute the values: 20.75 = 5 + (n-1) × 1.75
Step 4: Solve for n: 20.75 - 5 = (n-1) × 1.75, which gives 15.75 = (n-1) × 1.75
Step 5: Divide both sides by 1.75: n-1 = 15.75/1.75 = 9
Step 6: Therefore, n = 10