Question

A student decided to start saving money.On the first day he saved 1 cent, on the second day an additional 2 cents, on day 3 he saved 4 cents. Each day he doubled the amount he saved the previous day. How much would he be saving on day 20?
(Hint: The first term of the geometric sequence is 0.01 and the common ratio is 2. What is the 20th term?)

Question 1 options:

A-$3.80

B-$10,485.75

C-$5,242.88

D-$10,485.76

Answer 1

Answer:

The correct option is option (B).

He would be saving $10,485.75.

Step-by-step explanation:

We know that,

1 cent =$ 0.01.

Geometric sequence:

• The first term of the sequence be a and common ratio n, then $n^{th}$ term of the sequence is $T_n=a(r)^{n-1}$ .
• The sum of the sequence is

              $S_n=\frac{a(r^n-1)}{r-1}$    where r>1

                   $=\frac{a(1-r^n)}{1-r}$    where r<1

                   =na             where r=1

Here first term(a)= $0.01, r= 2 , n=20

$S_n=\frac{0.01(2^{20}-1)}{2-1}$

    =10,485.75

He would be saving $10,485.75.