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

The correct option is option (B).

He would be saving $10,485.75.

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=(a(r^n-1))/(r-1)` where r>1

`=(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=(0.01(2^(20)-1))/(2-1)`

=10,485.75

He would be saving $10,485.75.