6. Neela saves in a ‘Mahila Bachat gat’ Rs. 2 on the first day, Rs. 4 on the second day, Rs. 6 on the third day and so on. What will be her saving in the month of February 2010?
Solution:
The savings done by Neela on each day is as follows: $2, 4, 6, \dots$
These everyday savings form an Arithmetic Progression (A.P.) with:
- First day saving ($a$) = $2$
- Difference in savings made in two successive days ($d$) = $2$
- Total no. of days in the month of February 2010 ($n$) = $28$
$\therefore$ Total savings for the month of February ($S_{28}$) = ?
$$S_n = \frac{n}{2}[2a + (n - 1)d]$$
$$S_{28} = \frac{28}{2}[2(2) + (28 - 1)(2)]$$
$$S_{28} = 14[4 + 27(2)]$$
$$S_{28} = 14[4 + 54]$$
$$S_{28} = 14$$
$$S_{28} = 812$$
$\therefore$ Neela saved Rs. 812 in the month of February.