QUESTION

# Ramkali required Rs. 2500 after 12 weeks to send her daughter to school. She saved Rs. 100 in the first week and increased her weekly savings by Rs. 20 every week. Find whether she will be able to send her daughter to school after 12 weeks.

Hint: Find the series of money which is being saved every week. Use the formula of the sum of $n$ terms of an Arithmetic progression to determine the sum of saved money for 12 weeks. If the sum exceeds Rs. 2500 then she will be able to send her daughter to school otherwise not.
We know that sum of $n$ terms of an A.P is given by ${{S}_{n}}=\dfrac{n}{2}\left( 2a+(n-1)d \right)$. Therefore, substituting the value: $a=100,\text{ }n=12,\text{ }d=20$ in the above equation, we get,
\begin{align} & {{S}_{12}}=\dfrac{12}{2}\times \left( 2\times 100+(12-1)\times 20 \right) \\ & =6\times \left( 200+11\times 20 \right) \\ & =6\times \left( 200+220 \right) \\ & =6\times \left( 420 \right) \\ & =2520 \\ \end{align}