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Question
Ramkali would need ₹1800 for admission fee and books etc., for her daughter to start going to school from next year. She saved ₹50 in the first month of this year and increased her monthly saving by ₹20. After a year, how much money will she save? Will she be able to fulfil her dream of sending her daughter to school?
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Solution
Let a be the first term and d be the common difference.
We know that, sum of first n terms = Sn = \[\frac{n}{2}\][2a + (n − 1)d]
According to the question,
Saving of Ramkali in 1 year = ₹50 + ₹70 + ₹90.......
Here, a = 50, d = 70 − 50 = 20 and n = 12.
∴ S12 = \[\frac{12}{2}\][2 × 50 + (12 − 1)20]
= 6[100 + 220]
= 6 × 320
= 1920
Hence, After a year, she will save ₹1920.
Since, required amount for admission is ₹1800 and her savings will be ₹1920.
Thus, yes she will be able to fulfil her dream of sending her daughter to school.
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