Mathematics

Grade10

Easy

Question

# If the sum of three numbers in an Arithmetic Sequences is 9 and their product is 24, then numbers are……

- 2 , 4 , 6
- 1 , 5 , 3
- 2 , 8 , 4
- 2 , 3 , 4

Hint:

### The given question is about arithmetic progression. Arithmetic progression is a sequence of numbers where, the difference between two consecutive terms is constant. We are given that, the sum of three numbers from the sequence is 9. The product of the terms is 24. We will use the concept of common difference to solve the question.

## The correct answer is: 2 , 3 , 4

### The sum of the three terms is 9.

The product of the three terms is 24.

The common difference is denoted by d.

Common difference is the fixed difference between the consecutive numbers of the sequence. We have to add the common difference to the preceding term, to get the next term. Using this concept, we can write the terms as follows:

a – d , a, a + d

Sum of the terms is given as follows:

(a – d) + a + (a + d) = 9

a – d + a + a + d = 9

3a = 9

a = 3

Product of the terms is given as follows:

(a – d) × (a) × (a + d) = 24

Substituting the value of a in the above equation we get,

(3 – d)(3 + d)(3) = 24

Dividing both the sides by 3.

(3 – d)(3 + d) = 8

9 – d = 8

d = 1

d = 1

Taking a = 3 and d = 1

The terms are 3 – 1, 3, 3 + 1 = 2, 3, 4

Taking a = 3 and d = -1

The terms are 3 – (-1), 3, 3 +(-1) = 4, 3, 2

Therefore, the numbers in the sequence are 2, 3, 4 or 4, 3, 2.

For such questions, we should know the formula to find any number lf term.