Question

What value of k causes the terms 5, 2k, 13 to form an arithmetic sequence?

2
4
9/2
13/4

Answer 1

The correct answer is 3rd option 9/2

Explanation:

From the given sequence, 5, 2k, 13

Which are in AP.

We can consider a₁ = 5 , a₂ = 2k and a₃ = 13

To find the value of k

We have,

a₂ = (a₁ + a₃)/2

Here,

2k = (5 + 13)/2 = 18/2 = 9/2

Therefore the correct answer is option 3

9/2

Answer 2

`k=(9)/(2)`

Explanation:

The given sequence is

`5,2k,13`

For the sequence to be arithmetic, then

`2k-5=13-2k`

We group similar terms to get;

`2k+2k=13+5`

`4k=18`

Divide both sides by 4;

`k=(18)/(4)`

Simplify;

`k=(9)/(2)`