# Algebra/Number Theory

posted by .

In a sequence of four positive numbers, the first three are in geometric progression and the last three are in arithmetic progression. The first number is 12 and the last number is 452. The sum of the two middle numbers can be written as ab where a and b are coprime positive integers. Find a+b.

• Algebra/Number Theory -

The numbers are
12, 12+d, 12+2d, 452
12, 12+d, (12+d)r, (12+d)r^2=452

(12+d)r^2 = 452
12+2d = (12+d)r

so,

r = (12+2d)/(12+d)

(12+d)((12+2d)/(12+d))^2 = 452
(12+2d)^2 = 452(12+d)
d = 112.71
r = 1.09377

The numbers are

12, 124.71, 237.42, 452

## Similar Questions

1. ### math

Three numbers in an arithmetic sequence sum to six. If you add 1 to the first number, 2 to the second number, and 5 to the third number, the result will be a geometric sequence. What are the original 3 numbers?
2. ### math

There are two positive numbers that can be inserted between 3 and 9 such that the first three are in geometric progression while the last three are in arithmetic progression. Find the sum of those two numbers.
3. ### Maths

1..The first 2 terms of a geometric progression are the same as the first two terms of an arithmetic progression.The first term is 12 and is greater than the second term.The sum of the first 3 terms od the arithmetic progression is …
4. ### math

I would need help with example: The sum of three consecutive terms of geometric progression is 9. The first number with no change, the second number plus 12 and the third number minus 3, are the 3 consequtive terms of arithmetic progression. …
5. ### math

I would need help with example: The three numbers are consecutive terms of arithmetic progression and the sum of their second powers is 126. The first number 3 times smaller, the second number with no change and the third number 4 …
6. ### math

The first, the third and the seventh terms of an increasing arithmetic progression are three consecutive terms of a geometric progression. In the first term of the arithmetic progression is 10 find the common difference of the arithmetic …
7. ### algebra

three numbers are in harmonic progression. If the third number were decreased by 4 they would be in arithmetic progression. If the third number were decreased by 3 they would be in geometric progression. Find the third term of the …
8. ### math C2 sequences and series

The eight,fourth and second terms of an arithmetic progression form the first three terms of a geometric series. The arithmetic progression has first term A and common difference d, and the geometric progression has first term G and …
9. ### plz sequence sir steve reiny bob damon i need u

The three real,distint and non-zero numbers a,b,c are such that a,b,c are in arithmetic progression and a,c,b are in geometric progression. Find the numerical value of the common ratio of the geometric progression.. Hence,find an expression …
10. ### Algebra 2

In an infinite geometric progression with positive terms and with a common ratio |r|<1, the sum of the first three terms is 26/3 and the sum of the entire progression is 9. Determine the progression.

More Similar Questions