Question

Determine k so that 3k-2 2k2-5k + 8 and 4k+ 3 are the three consecutive terms of an AP

Answer 1

Answer:

Step-by-step explanation:

your answer is ready my dear

Answer 2

Answer: On solving the equation the value of K

K = 3 or K = 5/4

Step-by-step explanation:

Given that :

3k-2 2k2-5k + 8 and 4k+ 3 are the three consecutive terms of an AP

So, 2(2$k^{2}$-5k + 8) =  3k-2 + 4k+ 3

On solving the brackets

4$k^{2}$ -10k + 16 =  7k + 1

4$k^{2}$ -10k - 7k +16 - 1 =0

4$k^{2}$ -17k +15 = 0

Now , we can write - 17k as (-12k) + (-5k)

4$k^{2}$  - 12k - 5k +15 = 0

4k ( k - 3) -5 ( k - 3) = 0

(4k - 5)  (k - 3 ) = 0

Case 1 when,

(4k - 5) = 0

k = 5/4

Case2 ,when

k - 3 = 0

k = 3

So, the value of K will be 3 or 5/4

Additional knowledge:

An arithmetic progression (AP) is a mathematical sequence in which the difference between any two consecutive terms is constant. This constant difference is called the common difference and is represented by the variable "d". The first term in an AP is represented by the variable "a". The formula for finding the nth term of an AP is a + (n-1)d, where "n" represents the position of the term in the sequence.

For example, if the first term of an AP is 4 and the common difference is 2, the second term of the sequence would be 4 + (2-1)2 = 6, the third term would be 8, and so on. The sequence would be 4, 6, 8, 10, 12, etc.

APs are also useful for finding the sum of a certain number of terms in the sequence. The formula for this is n/2 (2a + (n-1)d), where "n" represents the number of terms in the sequence.

APs can be found in many real-world situations, such as counting numbers, even numbers, and multiples of a number. They are also frequently used in mathematical and scientific equations.

To learn more about arithmetic progression (AP) from the link below

https://brainly.in/question/11357684

To learn more about consecutive terms  from the link below

https://brainly.in/question/25671195

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