Question

To save money for a video game Ajay put 1 rupee in an envelope. Each day for 8 days he doubled the number of rupees from the day before. How much will he save on the eighth day?

Answer 1

Hint: We can form a geometric progression with first term equals to 1 and the common ratio equal to 2. Then we can find the 8th term of the GP using the equation for finding the nth term. The value of the 8th term will be the money he saved on the eighth day.

Complete step-by-step answer:
We are given that Ajay put 1 rupee on the 1st day. For the next day he doubles the money. We can say that he multiplied the money of the previous day with 2. So we can write it as a geometric progression.
$1,2,4,8,....$
This G.P. has first term $a = 1$and common ratio$r = 2$.
The nth term of a GP with 1st term a and common ratio r is given by
${a_n} = a{r^{n - 1}}$
So the 8th term is given by,
${a_8} = a{r^{8 - 1}}$
On substituting the values of a and r, we get
$ \Rightarrow {a_8} = 1 \times {\left( 2 \right)^7}$
$ \Rightarrow {a_8} = 128$
The money saved by Ajay on the 8th day will be equal to the 8th term of the G.P.
Therefore, the money saved by Ajay on the 8th day is Rs.128.

Note: Alternate approach to this problem is given by,
We can write the money he saved each day.
On the 1st day, he saved Rs.1.
On the 2nd day he saved Rs.2.
On the 3rd day, money saved$ = 2 \times 2 = Rs.4$
On the 4th day, money saved$ = 2 \times 4 = Rs.8$
On the 5th day, money saved$ = 2 \times 8 = Rs.16$
On the 6th day, money saved\[ = 2 \times 16 = Rs.32\]
On the 7th day, money saved$ = 2 \times 32 = Rs.64$
On the 8th day, money saved$ = 2 \times 64 = Rs.128$
Therefore, the money saved by Ajay on the 8th day is Rs.128.