### PROBLEM LINK:

**Author:** Mrinal Sinha

**Editorialist:** Mrinal Sinha

**Tester:** Amit Kumar Pandey

### DIFFICULTY:

EASY

### PREREQUISITES:

Math

### PROBLEM:

Starlord is stuck in space on his way back after a successful mission when his spacecraft crashed. He now has to go jumping from asteroid to asteroid to get to a nearby space camp. The asteroids are in such an order that their lengths increase to a certain extent as he jumps to the next asteroid. The series of the lengths of the asteroids is given below. For a given asteroid, you have to determine whether it comes in his path or not.

Series: 44, 120, 304, 736

### EXPLANATION:

The series given here is an Arithmetico-Geometrico Series with numbers written as 11 `*`

4, 15`*`

8, 19`*`

16 and 23`*`

32 respectively. Thus the first term of the A.P is 11 with common difference 4 whereas the first term of G.P is 4 with common ratio 2. With the help of above values we can determine the previous positive values which will be 7`*`

2 =14 and 3`*`

1 = 3.

Thus the general formula for the above expression is **(a+(n-1) *d)*(b*pow(r,n-1)),** where ‘a’ is the 1

^{st}term of the A.P (which is 3), ‘d’ is the common difference of the A.P (which is 4), ‘b’ is the 1

^{st}term of G.P (which is 1), ‘r’ is the common ratio of the G.P (which is 2) and ‘n’ is the n

^{th}term of the series.

Thus initialize n with 1 and calculate the value of above expression.

Thus initialize n with 1 and calculate the value of above expression.

*If the value is equal to the given number, then print **“YES”.**

- If the value is greater than the given number ,then print
**“NO”.**

*If the value is less than the given number, then increment n by 1 and again check whether the value of the expression is greater than or equal to the given number. Do this step until the 1^{st} or 2^{nd} step is satisfied.

### AUTHOR’S AND EDITORIALIST’S SOLUTIONS:

Author’s solution can be found here.

Editorialist’s solution can be found here.

Tester’s solution can be found here.