Split 207 into three parts such that these are in AP and the product of the two smaller parts is 4623.

Given: Product of three part = 4623

To find: Three parts.

Formula Used: nth term of an AP is:

a_{n =} a + (n - 1) d

Explanation:

Let the three parts of the number 207 are

a₁ = a - d

a₂ = a

a₃ = a + d

Clearly a₁, a₂ and a₃ are in AP with common difference as d.

Now, by given condition,

Sum = 207

a₁ + a₂ + a₃ = 207

( a - d ) + a + ( a + d ) = 207

3a = 207

a = 69

Also,

a₁a₂ = 4623

( a - d )a = 4623

( 69 - d )69 = 4623

69 - d = 67

d = 69 - 67

d = 2

Hence, required three parts are 67, 69, 71.