For what value of 'K' the number 3K + 2, 4K +3 and 6K - 1 are the consecutive terms of an A.P.
you need a common difference, so
(4k+3)-(3k+2) = (6k-1)-(4k+3)
To find the value of 'K' for which the numbers 3K + 2, 4K + 3, and 6K - 1 form an arithmetic progression (A.P.), we need to determine if the common difference between consecutive terms is the same.
The common difference (d) between consecutive terms in an arithmetic progression is calculated by subtracting any term from its previous term. Therefore, we can calculate the common difference of the given terms by subtracting the second term from the first term and the third term from the second term.
Common Difference (d):
= (4K + 3) - (3K + 2)
= 4K + 3 - 3K - 2
= K + 1
Next, we will check if the common difference is same when calculated between the second and third term:
Common Difference (d):
= (6K - 1) - (4K + 3)
= 6K - 1 - 4K - 3
= 2K - 4
For an arithmetic progression, the common difference should be the same for all consecutive terms. Therefore, we equate both the common differences and solve for 'K'.
K + 1 = 2K - 4
By solving the equation, we can find the value of 'K':
K + 1 = 2K - 4
Subtract K from both sides:
1 = K - 4
Add 4 to both sides:
5 = K
Hence, the value of 'K' for which the numbers 3K + 2, 4K + 3, and 6K - 1 form an arithmetic progression is K = 5.