Question

find the value of k for which (3k+4),7k,and (9k+4) are AP

Answer 1

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Answer 2

Given,

(3k+4),7k, and (9k+4) are the three terms in AP.

To find,

The value of k.

Solution,

If the numbers are in Arithmetic Progression then the common difference between the terms is equal.

Consider three terms a1, a2, a3 are in AP then the common difference (d) is simply calculated as a2 - a1, or a3 - a2.

Similarly, in the given arithmetic progression common difference (d) would be equal and can be calculated as-

⇒   (7k)-(3k+4) = (9k+4)-(7k)

⇒   7k-3k-4 = 9k+4-7k

⇒   4k-4 = 2k+4

⇒   4k-2k = 4+4

⇒   2k = 8

⇒    k =4.

Hence, the value of k for which (3k+4),7k, and (9k+4) are the three terms in AP is k =4.