Question

if k,2k-1,2k+1 are three consecutive terms of an AP,find k?

Answer 1

If a,b, c are in Ap
b-a = c-b-----(1)

According to the given problem
a=k, b=2k-1, c=2k+1
Using (1)

(2k-1) - k = (2k+1)-(2k-1)
2k-1-k =2k+1-2k+1
k-1 = 2
k=2+1
k=3

Answer 2

Answer:

The value of k is 3.

Step-by-step explanation:

Step 1: The given three terms in arithmetic progression is K, 2k-1, 2K+1

Step 2: Assigning the variables in the given three terms in Arithmetic Progression

Step 3: Assign k value in P variable, 2k-1 value in a Q variable, 2k+1 value in R variable.

P=k, Q=2k-1, R=2K+1

To find the value of k

Using formula:

(Q-P)=(R-Q) [Subtract the value of Q and the value of p is equal to subtract the value of R and the value of Q]

(2k-1)-(K)=(2K+1)-(2K-1)

2K-1-K=2K+1-2K+1

2K-1-K=2

K=2+1 [substitute the value in given terms to find the value the value of k]

K=3