Mathematics

Grade10

Easy

Question

# For what value of K the series 2 , 3 + K and 6 are in Arithmetic Sequence?

- 4
- 1
- 2
- 5

Hint:

### We are given a sequence. We have to find the value of K such that the given sequence is an arithmetic progression. Arithmetic progression is a sequence of numbers where, the difference between two consecutive terms is constant. We use the properties of the sequence to find the value of K.

## The correct answer is: 1

### The given sequence is 2, 3 + K, 6.

The difference between two consecutive terms of the arithmetic progression is constant. It is called as common difference. We will use this concept to solve the question.

Let’s find the difference between the first and second term.

a_{2} - a_{1} = 3 + K – 2

= 1 + K

The difference between third and second term is as follows:

a_{3} – a_{2} = 6 – (3 + K)

= 6 – 3 – K

= 3 – K

Now, using the concept of common difference we can write

a_{2} - a_{1 }= a_{3} - a_{2}

1 + K = 3 – K

2K = 2

K = 1

So, for K = 1 the given sequence is an arithmetic progression.

For such questions, we should know the concept of common difference.