Jhon has purchase 20 books, the 1st book cost 1 dollar, the 2nd, 2 dollar, the 3rd, is 4 dollar and the 4th, 8 dollar and so on. How much did jhon pay for books? 

The prices of the books follow a geometric sequence. To find the total amount John paid for the 20 books, we need to calculate the sum of the first 20 terms of this geometric sequence.

### Given:
- The first term $ a_1 = 1 $ (the cost of the 1st book)
- The common ratio $ r = 2 $ (since each book costs twice as much as the previous one)

### Formula for the sum of the first $ n $ terms of a geometric sequence:

\[
S_n = a_1 \cdot \frac{r^n - 1}{r - 1}
\]

### Substituting the given values:

\[
S_{20} = 1 \cdot \frac{2^{20} - 1}{2 - 1} = 2^{20} - 1
\]

Now, calculate $ 2^{20} $:

\[
2^{20} = 1,048,576
\]

So:

\[
S_{20} = 1,048,576 - 1 = 1,048,575
\]

### Conclusion:

John paid a total of **$1,048,575** for the 20 books.

Would you like more details or have any questions about this? Here are some related questions:

1. What would be the cost of the 21st book?
2. How much did John pay for the first 10 books?
3. If the common ratio were 3 instead of 2, how much would John have paid for 20 books?
4. How would the total change if John only bought the first 15 books?
5. What is the general formula for the cost of the nth book in this sequence?

**Tip:** In a geometric sequence, the sum of the terms can grow rapidly, especially when the common ratio is greater than 1.

Learn how to calculate the total cost for 20 books in a geometric sequence where each book's price doubles from the previous one. John paid a total of $1,048,575. This problem involves geometric sequences and the sum of series formula. Suitable for Grades 10-12 students.

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