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To inculcate the good habit of savings in her children, Reema brought a piggy bank and after putting a ₹ $10$ coin in it, she handed it over to her daughter Amisha and asked as to put money in it from her pocket money at the beginning of every week. Amisha put two ten rupee coins at the beginning of next (second) week and in this way increases her savings by one ₹ $10$ coin every week. Based on the above, answer the following questions : (a) How many coins were added in the piggy bank at the beginning of $5^{th}$ week ? (b) How many ₹ $10$ coins will be there in the piggy bank after the end of $7$ weeks ? (c) (i) If the piggy bank can hold a maximum of $300$ ₹ $10$ coins, after how many weeks it would be full ? OR (c) (ii) Find the total amount of money in the piggy bank at the end of $20$ weeks.
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(a) $a_5 = 1 + 4(1) = 5$
(b) $S_7 = \frac{7}{2} [2 + 6 \times 1] = 28$ coins
(c) (i) $S_n = \frac{n}{2} [2 + (n - 1) \times 1] = 300 \implies n = 24$ weeks
OR
(c) (ii) $S_{20} = 10[20 + 19 \times 10] = \text{\text{Rs} } 2100$
(b) $S_7 = \frac{7}{2} [2 + 6 \times 1] = 28$ coins
(c) (i) $S_n = \frac{n}{2} [2 + (n - 1) \times 1] = 300 \implies n = 24$ weeks
OR
(c) (ii) $S_{20} = 10[20 + 19 \times 10] = \text{\text{Rs} } 2100$