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Question: Tommy wanted to buy a gold ring which costs $121 by saving money. His first day savings are $6. Each succeeding day he saves $1 more than the previous day. With this pattern of savings, in how many days can he buy the ring?


A ) 11
B ) 115
C ) 22
D ) 116

Steps to derive

1 The money Tommy saves increases by $1 each day. So, daily savings form an arithmetic sequence: 6, 7, 8, 9, .....
 [Analyse and understand the problem.]

2 Let $121 will be the sum to n terms of an arithmetic series.

3 Sn = n[2a1 + (n -1) d]2
 [Write the formula for the sum of an arithmetic series.]

4 121 = n[2(6) + (n-1)1]2
 [Replace Sn = 121, a1 = 6, d = 1.]

5 242 = n[12 + n -1]
 [Cross multiply.]

6 242 = n2 + 11n
 [Simplify.]

7 n2 + 11n - 242 = 0

8 n = 11, - 22
 [Solve for n.]

9 So, Tommy can buy the ring in 11 days.
 [The number of days cannot be negative and so, n = - 22 is not possible.]



Hence the right answer is Option A

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