Question

what will be the value of k so that 2k+1, 5k-3 and -8+5 are three consecutive terms of a AP

Answer 1

Given,

2k+1, 5k-3, and -8k+5

To Find,

The value of k so that 2k+1, 5k-3, and -8k+5 are three consecutive terms of an AP =?

Solution,

We can solve the question as follows:

We have to find the value of k so that 2k+1, 5k-3, and -8k+5 are three consecutive terms of an AP.

For a series of terms to be in arithmetic progression, the difference between two consecutive terms is always a constant.

Here, for the terms to be in A.P. the difference between 2k+1, 5k-3 and 5k-3, -8k+5 should be equal.

Therefore,

$(5k-3) - (2k+1) = (-8k+5) - (5k-3)$

We will solve the above equation and find the value of k.

$5k - 3 -2k - 1 = -8k + 5 - 5k + 3$

$3k - 4 = -13k + 8$

$3k + 13k = 8 + 4$

$16k = 12$

$k = \frac{12}{16} = \frac{3}{4}$

Hence, the value of k is equal to 3/4.