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.

Question

Homi · Accepted Answer

We will use the formula for the nth term of an arithmetic progression to find the week number.

Step 1 — Identify the AP terms

Ramkali saved ₹ 5 in the first week. This is our first term, $a$ . Her weekly savings increased by ₹ 1.75. This is our common difference, $d$ . Her savings in the nth week became ₹ 20.75. This is our $a_n$ .

Step 2 — Apply the AP formula

We use the formula for the nth term of an AP. The formula is $a_n = a + (n-1)d$ . Let's substitute the values we know.

$20.75 = 5 + (n-1)1.75$

Now, let's solve for $n$ .

$20.75 - 5 = (n-1)1.75$

$15.75 = (n-1)1.75$

$(n-1) = \frac{15.75}{1.75}$

$(n-1) = 9$

$n = 9 + 1$

$\boxed{n = 10}$

Answer

The value of $n$ is 10.

Question 20

Answer

More questions in Exercise 5.2