# Three numbers form an arithmetic sequence having a common difference of 4. If the first number is increased by 2, the second number by 3, and the 3rd number by 5, the resulting numbers form a geometric sequence. How do you find the original numbers?

##### 1 Answer

May 1, 2016

#### Explanation:

The original sequence is:

#a_1 = a#

#a_2 = a+4#

#a_3 = a+8#

The modified sequence is:

#b_1 = a+2#

#b_2 = a+7#

#b_3 = a+13#

Since

#b_2^2 = b_1 b_3#

#a^2+14a+49 = (a+7)^2 = (a+2)(a+13) = a^2+15a+26#

Subtracting

#a=23#

So